The only reasonable explanation for a people that survived approximately 200,000 years or more to have gone extinct after cromagnon showed up is that the Cromags killed them off, some interbreeding some slaughter, it is the Homo Sapien way.
Neanderthals were killed off in a neolithic world war which probably lasted several generations, but not thousands or tens of thousands of years. Neanderthals were Europe's apex predator; the main body of them in Europe ate a diet which was over 90% meat including themselves and any other hominids or humans they could catch. Their DNA was roughly halfway between ours and that of a modern ape, their skulls were those of apes with huge eyes for nocturnal hunting, they had the same 6" fur coat as every other ice age animal which is why no needles have ever been found with Neanderthal remains, and this is what they looked like:
Image courtesy of www.themandus.org
Danny Vendramini on youtyube:
http://www.youtube.com/watch?v=mZbmywzGAVs
No living human is related to Neanderthals in any way and the reason for that should be fairly obvious...