The Oriental Orthodox Churches
Very sadly, despite the Henotikon, the condemnation of the Three Chapters, and the other efforts of the Fifth Council to win back the Non-Chalcedonians, they were not reunited to the Byzantine Church. By 553, their alternate ecclesiastical hierarchical structure was already quite firmly established—a process which actually had not begun until the decade of the 530s. The Non-Chalcedonians generally felt that the efforts of the Fifth Council were too little, too late. Apparently they never became convinced that Chalcedon was faithful to the thought of Saint Cyril. Even though Chalcedon reaffirmed the Third Council’s condemnation of Nestorius, the Non-Chalcedonians always suspected that the Chalcedonian Definition tended towards Nestorianism.
One major reason for their suspicion was that Chalcedon also had restored several bishops to their thrones who had been deposed at the Robber Council—bishops who at one time did have pro-Nestorian leanings, especially Bishop Theodoret of Cyrrus and Bishop Ibas of Edessa. Even though the pro-Nestorian writings of these two bishops were condemned at the Fifth Council, this was not enough to satisfy the Monophysites.
The disagreement was never settled, despite further efforts on the part of the Byzantines to win back the non-Chalcedonians in the next century. And while there have been encouraging discussions between the two sides in recent times (beginning in the 1960s), in which basic doctrinal agreement seems to have been established, the dissenters from the Chalcedonian decision remain separated from the Orthodox Church.
Today, the Non-Chalcedonian Churches are generally known as the Oriental Orthodox Churches. They are the Coptic Church of Egypt, the Ethiopian Church, the Syrian Jacobite Church, the Syrian (Malankara) Church of India, and the Armenian Church.