The Definition of the Council of Chalcedon was not accepted by the extreme disciples of Saint Cyril of Alexandria, nor by those who later came to be associated with them. These Christians were called by the Chalcedonians Monophysites, because of their insistence on Saint Cyril’s phrase “one nature of the Word of God Incarnate” (“one nature” in Greek is “mia physis”). Hence they rejected the Chalcedonian Definition, which speaks of Christ being “in two natures.”
The supporters of Chalcedon claimed and still claim that the Chalcedonian Definition is fully in accord with the thought of Saint Cyril, who did not insist on the Monophysites’ hallmark phrase “one nature of the Word of God Incarnate” in his letters to Nestorius, or at the Council of Ephesus, or in the Formulary of Peace. And from other things he wrote, it is clear that when he used this problematic phrase, his actual meaning was “one hypostasis of the Word of God Incarnate,” which is just what Chalcedon proclaimed and defended.