St. Hegesippus (c. AD 110 - c. 180), according to Eusebius, was from the east. He was most likely a Hellenistic Jew. He is quoted by Eusebius in his Ecclesiastical History. First Eusebius says the following about St. Hegesippus.
Hegesippus in the five books of Memoirs which have come down to us has left a most complete record of his own views. In them he states that on a journey to Rome he met a great many bishops, and that he received the same doctrine from all. It is fitting to hear what he says after making some remarks about the epistle of Clement to the Corinthians.
St. Hegesippus had come to Rome apparently because of the rise of gnostic heresies. It is possible that he either wanted to determine what the church at Rome was teaching about these things, or that he was concerned that these things might influence the church at Rome. Notice that according to St. Hegesippus, during his travels to Rome he met a great many bishops and received the same doctrine from them all. This testifies that the faith that had been handed down by the Apostles had been preserved throughout Asia, Greece and Italy well into the latter part of the second century. Otherwise there would have been various accounts of the faith between the various bishops.
Eusebius then quotes from St. Hegisippus:
And the church of Corinth continued in the true faith until Primus was bishop in Corinth. I conversed with them on my way to Rome, and abode with the Corinthians many days, during which we were mutually refreshed in the true doctrine. And when I had come to Rome I remained there until Anicetus, whose deacon was Eleutherus. And Anicetus was succeeded by Soter, and he by Eleutherus. In every succession, and in every city that is held which is preached by the law and the prophets and the Lord.
St. Hegesippus describes his visit with the Corinthian church in a way that indicates that the problems with Primus were already in the past. He was able to be mutually refreshed with them in "the true doctrine". St. Anicetus became bishop of Rome around AD 155, so St. Hegesippus stayed in Rome from around that time until the time that St. Eleutherus became bishop of Rome. But the fact that he is writing about St. Eleutherus as bishop of the church at Rome shows that he was writing this no earlier than AD 175, because St. Eleutherus was the bishop of Rome from AD 175 - 189. St. Hegesippus is reporting (writing no earlier than AD 175) that what is believed in every city is what is "preached by the law and the prophets and the Lord". But St. Hegesippus tells us the following about the rise of the gnostic false teachers:
And after James the Just had suffered martyrdom, as the Lord had also on the same account, Symeon, the son of the Lord's uncle, Clopas, was appointed the next bishop. All proposed him as second bishop because he was a cousin of the Lord. Therefore, they called the Church a virgin, for it was not yet corrupted by vain discourses. But Thebuthis, because he was not made bishop, began to corrupt it. He also was sprung from the seven sects among the people, like Simon, from whom came the Simonians, and Cleobius, from whom came the Cleobians, and Dositheus, from whom came the Dositheans, and Gorthæus, from whom came the Goratheni, and Masbotheus, from whom came the Masbothæans. From them sprang the Menandrianists, and Marcionists, and Carpocratians, and Valentinians, and Basilidians, and Saturnilians. Each introduced privately and separately his own peculiar opinion. From them came false Christs, false prophets, false apostles, who divided the unity of the Church by corrupt doctrines uttered against God and against his Christ.(E.H. 4.22.4)
What exactly does St. Hegesippus mean when he says that the Church began to be corrupted? He means that certain false teachers began to make their way into the Church, and lead some people astray, and cause divisions. But he does not mean that the Church as a whole fell away. He is speaking as someone who has retained the "true faith", and has found the true faith present in every church where he has traveled. So this corruption about which he is speaking was apparently caused by sects arising almost parasitically in certain particular churches. The Church had to struggle against these various false teachers in a more pronounced way, because the Apostles had passed away, and even those persons who had known the Apostles were, after St. Polycarp's martyrdom, also gone.
So St. Hegesippus indicates to us that while there was a rise of false teachers, there was at the same time a struggle on the part of the Church to preserve orthodoxy, which it did. St. Hegesippus is testifying to the continuation of orthodoxy throughout the Catholic Church well into the latter part of the second century. He gives us testimonial evidence of a continuum of orthodoxy, with lapses here and there by individual bishops and presbyters, but an overall uniformity in the faith into the latter part of the second century.