Thoughts poured through our heads of all those other impotent crowds who had watched similar menacing processions in the capitals of Europe during the past 70 years, often weeping (or later wishing that they had wept).
It was a vision of pure power, stirring and moving for a moment, then infinitely sad as you realised that this power was not yours, but an enemy's.
I lived in the Russian capital for more than two years during the nervous, burnt-out end of the great socialist experiment, an experiment that had turned a sixth of the planet into a laboratory of death, lies and failure, and which people today are inclined to forget - not realising that the ideas that lay behind that colossal wreck are still very much alive.
For most of my life, Soviet tanks had been the hard steel symbol of militant socialism on the march, showing the true face of that supposedly benevolent creed.
They were the ultimate example of what happens when force is stronger than law.
They represented the sneer of cold command, the Left's self-righteous belief that the people should get what was good for them, hot and strong, whether they liked it or not.
Their main purpose since 1945 had been to crush liberty in East Berlin, Budapest and Prague.
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History repeated: Msta self-propelled howitzers in Red Square for Victory Day on Friday
Now that arrogance - once concentrated under the Red Flag - has dispersed into the worldwide doctrines of political correctness which squash free thought more surely and more widely than any tank, and are even harder to resist.
But that August morning I was surprised, mainly because I thought I had already seen the last of them.
A few months before, in November 1990, I had stood just to the left of Lenin's Tomb in Red Square and witnessed the great iron ballet that was the Revolution Day parade.
An uncomfortable Mikhail Gorbachev, just yards away, took the salute from the top of the mausoleum, surrounded by the nastiest symbols of the cruel system he was honestly trying to reform.
Many then suspected, but nobody knew, that this display would never happen again.
But within a few months the power of the Communist Party was finally broken and it was announced that there would not be another parade.
I was pleased to have seen it, and even more pleased that the miserable global disaster of Lenin's seizure of power would no longer be celebrated, when it really ought to be mourned.
So I was astonished and a little alarmed a few months ago to learn that the parade was being revived.
Was it, as some have claimed, the start of a new Cold War? Was Russia on the way back to Bolshevism?
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Turning back time: Tanks parade in front of Lenin's mausoleum in Soviet days
At first sight, it seemed as if it might be so.
On Friday I watched the tanks clatter through Red Square once again - Lenin's Tomb had been carefully concealed behind a giant billboard urging us to remember 1945 and no further back than that.
I jumped as the great cannons thundered out their salute from under the Kremlin walls.
I felt slightly queasy as the gargantuan, bulging tractors carrying Topol ballistic nuclear missiles made their rapid, sinister way past St Basil's Cathedral.
These things, in some now unimaginable catastrophe of chaos or unbalanced rage, might conceivably be used against me and mine.
I was moved by the detachments dressed in the Second World War helmets and tunics of the Red Army, who despite being endlessly betrayed by their foul leader and squandered by their inhuman generals, should always be remembered as one of the great examples of valour in the history of mankind.
I simultaneously admired and disliked the rigid Prussian drill, the slanted, set faces, the deep, orchestrated roars of "Urrah", and smiled to myself as Defence Minister Anatoly Serdyukov made his way round the square in an open-topped Zil limousine.
Serdyukov, who is by no means slender, has made himself unloved among Russian generals by suggesting that these generously-built old crocodiles go on a fitness regime and cut out the pancakes and sour cream.
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Who's in charge? Putin and Medvedev watch the Victory Day parade this week
It crossed my mind that the parade would have been less impressive but more realistic if it had featured some sections of gas pipeline, with workmen on top of them shutting the valves, and a few oil derricks guarded by some secret policemen in Armani suits and dark glasses.
These are the real sources of power in Russia, and the only power with which she can now menace her neighbours.
Modern Moscow is, of course, nothing like the city I knew 18 years ago.
Clean and prosperous where it had been filthy and poor, it now shimmers like a kind of Russian Hong Kong - great piles of gross wealth with a seething underside of hollow-faced desperation if you stray from the main centres.
But in preparation for the big parade, the city was plastered with posters urging celebration of the Day of Victory, Friday May 9, which the Soviet Union always claimed was the true VE Day.
Many of these placards featured Soviet symbolism - hammers and sickles, the medal ribbons of the old Red Army, red stars and red flags.
Cinemas and TV stations - and even a screen in the main shopping street - showed Second World War films of Stalinist heroism.
The haunting old Soviet national anthem - totalitarians always have the best tunes - was frequently played on TV.
And on Wednesday, the shifty, faintly ridiculous transfer of power from President Vladimir Putin (5ft 5in) to his even smaller successor Dmitri Medvedev (5ft 4in) confirmed that Russia has ended its brief flirtation with freedom and democracy, and is now a cynical autocracy with a laughable window-dressing of democratic forms.
To the hollow laughter of all who listened at home, Comrade President Medvedev vowed to strengthen the rule of law in this wholly lawless, desperately corrupt country.
Few believe he will have real power, which will remain with Prime Minister Putin or whoever really controls him.
Perhaps that is why the new President never donned his chain of office, which sat on a table next to him during the ceremony.
Cruel rumour suggested that the chain is so long it would have hung embarrassingly round his knees. There is clearly some sensitivity about his lack of inches.
On TV, Medvedev somehow appeared to be the same height as Putin. Some wags sneered that he was standing on the constitution.
But there are several deep differences between the old Kremlin and the new one, to which we should pay more attention.
The new Russia is without doubt an authoritarian state. Its parliament is a joke, controlled by an official government party and with an "opposition" that is wholly fraudulent (remind you of anywhere?).
Its media have been terrified or blackmailed into servility, except for a couple of small newspapers and a couple of radio stations, which reach almost nobody.
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Aerial threat: Warplanes swoop above Kremlin churches
But as long as you leave the government alone, you can say and think what you like in private.
In fact, I would venture that in some ways speech is freer than it is in the politically-correct West, where an individual's career can be destroyed, or he can be questioned by the police, if he ventures an unapproved opinion of homosexuality or feminism.
Listen to the excellent Vladimir Ryzhkov who, the last time I met him, was one of the few genuinely independent members of the Duma, the Russian parliament.
He is now a politician without a role, disqualified from the last elections because the authorities simply declared that his party was "too small".
There are no constituencies here any more - too much risk of a brave individual winning.
Instead Russia has the party list system that New Labour is stealthily bringing to Britain. So no officially authorised party, no seat.
Ryzhkov is deeply, scornfully critical of the government and the state of the country, saying of Putin: "I have known him since 1996, when he was just a bureaucrat.
"When I left his office I immediately forgot everything about him. I could remember the room and his secretary, but I couldn't remember anything about him.
"This is a classic petro-state, like Iran. It is totally corrupted. Corruption is now valued at £140billion a year - we are one of the three most corrupt nations on Earth, in the same class as Nigeria.
"We are also becoming like Brazil, with a small superrich class of 130 dollar billionaires and a huge poor class, with a quarter of the people living on less than a pound a day. You can see them on the Moscow Metro."
The poor respond, as they have always done, by reaching for the vodka bottle.
"This is the most alcoholic era in Russian history, worse than the days of Leonid Brezhnev," says Ryzhkov. "There is apparent prosperity but cultural degradation.
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Target audience: Muscovites perch on barriers and climb lampposts to watch the parade
"We appear richer and stronger but our social capital, such as education, is deteriorating. One day there will be a very big crisis."
But at present such a crisis seems far away because high oil and gas prices mean money is constantly shovelled into the hands of the powerful and they can afford to let some of it trickle down to the poor.
"It's neo-Brezhnev time, like the 'golden time' of 1973 and 1974 when suddenly there was chocolate and meat in the shops because the price of oil was so high," says Ryzhkov.
But he cautions against taking the parallel with the old USSR too far: "Private life is free. This is the big difference. The political system is like the Soviet Union. TV is like the Soviet Union. But private life is now free. Why go back to the old ways?
"Too much control of private life destabilised the regime. They understand that an authoritarian regime is more stable than a totalitarian regime. People can be free as long as they don't touch politics."
Ryzhkov says this should be a warning to the foolish people in the United States and Western Europe who hope a richer China will be a free China.
"The idea that if you have a Mercedes you will become a citizen and a supporter of freedom just isn't true. There is no direct connection between pockets and freedom."
As for the military parade, Ryzhkov thinks it silly for the West to worry.
"The tanks are for domestic reasons. Russians like tanks, rockets and missiles. We like to be great, even if we aren't really.
"We like you to be afraid of us and we are happy to appear as monsters. The real situation in the Russian army is very bad but Russians have to believe it is strong."
Alexander Golts, a military analyst, explained just how useless the Russian military now is.
"This parade has nothing to do with reality. It is a big show. When I ask myself why the Russian military exists now, I cannot answer.
"They cannot fight a high-tech war or a low-intensity war. Instead, they have become the most efficient instrument of government propaganda.
"This is the best way of showing Russians that their country is getting up off its knees, as our leaders love to say it is."
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Loud and clear: Sailors from the Russian navy join in Friday's military demonstration
Golts agrees with Ryzhkov that the Red Square display is aimed at Russians.
"The main idea of the old Soviet parades was to impress the West and show you the might we had. Today everybody in the West and all experts know that the Russian military is not real.
"Russian citizens don't know much about the Russian military. So this is for domestic propaganda. It is an opportunity for our leaders to show up and assure citizens that we are a superpower."
The modern T-90 tanks and the shiny new planes are prototypes that are not in serial production because the industrial system has gone wrong.
The army cannot even get enough soldiers, either as volunteers or conscripts. "There's still one officer for every two soldiers," says Golts.
"Trying to avoid military service has become a national sport. There is an unbelievable corruption machine.
"There are thousands of fake medical certificates and whole institutes of higher education that exist so that their students can get exemption from the army, and which have absurdly low academic standards.
"The falling birthrate will soon create a complete crisis as there just aren't enough teenage boys."
This explains the enormous posters on the way into Red Square that proclaim this is "The Year Of The Family".
Others, with a message that translates roughly as "Make Love, Russia Needs You", show smiling young women displaying large broods.
Perhaps they will go back to the Stalinist days of "Heroine Mothers" who won well deserved medals and special privileges in the sausage queue for having ten children.
Even more scornful of the show is Ilya Yashin, 24, chairman of the youth branch of Yabloko, the last surviving democratic party of any size.
"I am in favour of celebrating this victory but it is supposed to be a holiday for those who won this victory for us. Most of them will die before their pensions are increased as the government has promised," he said.
"Forty per cent of veterans live in poverty while we waste money on the army.
"More than £20million will be spent on cleaning up Moscow after this event. It is cynical to do this when veterans are living in poverty, when our army is eaten up by corruption and the bullying of young recruits. This is just propaganda, just empty."
Yashin is, of course, quite right. The current fashion for pretending that there is a new Cold War is ridiculous.
Russia is a catastrophic country, Nigeria with rockets, mainly dangerous to herself and mainly concerned about herself.
The problems that we have had with her have come because we have got mixed up in internal struggles that we did not understand, or because of vainglorious attempts to push our way into parts of Europe where we have no real power to enforce our will, just the power to irritate Moscow.
The real lessons to be learned from Russia's sad slide back into the darkness are different and require us to look closely at ourselves.
How secure are our own freedoms in an age when "Security" is the pretext for an unending assault on liberty, and when intolerant Left-wing thought rules in most of the media, schools and universities?
Do we really value them any more highly than the millions of Russians who now opt for a quiet life?
Did the disappearance of the Soviet Union, whose ugliness discredited Marxism as long as it existed, make it easier for Left-wing ideas and policies to take root in our societies in new, more persuasive forms?
Sadly, I conclude that we in Britain were safer by far when the glum old Politburo still took the salute on top of Lenin's Tomb and the tanks and missiles still bore the hammer and sickle.
As for poor, poor Russia, I can only hope that one day it may be happy - but in the meantime I think I need, much more urgently, to worry about my own country.
And, the Hammer & Sickle in the Red Star is ever present still.
