Some more from Irenaeus:
"It is possible, then, for everyone in every church, who may wish to know the truth, to contemplate the tradition of the apostles which has been made known to us throughout the whole world. And we are in a position to enumerate those who were instituted bishops by the apostles and their successors down to our own times, men who neither knew nor taught anything like what these heretics rave about" (Against Heresies 3:3:1 [A.D. 189]).
http://www.catholic.com/library/Apostolic_Succession.asp
"But since it would be too long to enumerate in such a volume as this the successions of all the churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient church known to all, founded and organized at Rome by the two most glorious apostles, Peter and Paul—that church which has the tradition and the faith with which comes down to us after having been announced to men by the apostles. For with this Church, because of its superior origin, all churches must agree, that is, all the faithful in the whole world. And it is in her that the faithful everywhere have maintained the apostolic tradition" (ibid., 3:3:2).
"Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true. To these things all the Asiatic churches testify, as do also those men who have succeeded Polycarp down to the present time" (ibid., 3:3:4).
"[I]t is incumbent to obey the presbyters who are in the Church—those who, as I have shown, possess the succession from the apostles; those who, together with the succession of the episcopate, have received the infallible charism of truth, according to the good pleasure of the Father. But [it is also incumbent] to hold in suspicion others who depart from the primitive succession, and assemble themselves together in any place whatsoever, either as heretics of perverse minds, or as schismatics puffed up and self-pleasing, or again as hypocrites, acting thus for the sake of lucre and vainglory. For all these have fallen from the truth" (ibid., 4:26:2).
"The true knowledge is the doctrine of the apostles, and the ancient organization of the Church throughout the whole world, and the manifestation of the body of Christ according to the succession of bishops, by which succession the bishops have handed down the Church which is found everywhere" (ibid., 4:33:8).
Thanks for the post and ping!
"Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true.
Martyrdom of St. Peter
Then as the first decrees were followed by others commanding that those in prison should be set free, if they would sacrifice, but that those who refused should be tormented with countless tortures; who could again at that time count the multitude of .martyrs throughout each province, and especially throughout Africa and among the race of the Moors, in Thebais and throughout Egypt, from which having already gone into other cities and, provinces, they became illustrious in their martyrdoms.
Diocletian: Edicts Against The Christians