Not long after the Council of Ephesus had condemned the heresy of Nestorius concerning the two persons of Christ in 431, had the opposite error of the Nestorian heresy arose. Since Nestorius so fully divided the Divine and the human in Christ that he taught a double personality or a twofold being in Christ, it became incumbent on his opponents to emphasize the unity in Christ and to exhibit the God-man, not as two beings but as one. Some of these opponents in their efforts to maintain a physical unity in Christ held that the two natures in Christ, the Divine and the human, were so intimately united that they became physically one, inasmuch as the human nature was completely absorbed by the Divine. Thus resulted one Christ not only with one personality but also with one nature.
The Third Ecumenical Council, held at Ephesus, did not put an end to the debate over the Person of Christ, failing to reconcile those sympathetic to Nestorius with the Church. Not long afterwards, however, in the 430s, a reconciliation was attained by means of a union, i.e., a unification which, for all intents and purposes, brought an end to the division within the Church. John of Antioch [previously a follower of Nestorius], in the name of all the bishops of the region of Antioch, sent to Saint Cyril a confession of faith, the essence of which is included in the following excerpt : We [wrote the Antiochian bishops] confess, therefore, our Lord Jesus Christ, the only-begotten Son of God, perfect God, and perfect man of a reasonable soul and flesh consisting; begotten before the ages of the Father according to His divinity, and in the last days, for us and for our salvation, [was born] of the Virgin Mary according to His humanity; that He is consubstantial with the Father according to divinity and consubstantial with us according to humanity, for in Him there is a perfect unity of two natures. For this reason do we also confess one Christ, one Son, one Lord. According to this understanding of such an unconfused union, we confess the all-holy Virgin to be the Theotokos; because God the Word was incarnate and became man, and in His very conception He united Himself to the [bodily] temple received from her. We know the theologians make some things of the evangelical and the apostolic teaching about the Lord common as pertaining to the one Person, and other things they divide as to the two natures, and attribute the worthy ones to God on account of the Divinity of Christ, and the lowly ones to His humanity.
At the end of the epistle there is an anathematization of Nestorius and his doctrine, with a declaration to the effect that Maximian is received into communion. Cyril of Alexandria accepted this confession of John and the bishops of like mind with him as a gift from heaven, acknowledging it as wholly Orthodox. Peace began to spread throughout the ecclesiastical world, and disputes began to die down.
Those who held Saint Cyril in high respect however were the forerunners of the soon to be revealed Monophysite heresy. They considered the communion between Saint Cyril and John of Antioch to be a betrayal of Orthodoxy and perceived heresy in the teaching of Saint Cyril on the two natures in Christ. Despite their great number, they behaved with restraint while Saint Cyril was alive, for he enjoyed tremendous respect with the Church. But with his death matters changed...
http://www.goholycross.org/studies/councils.html#Fourth
