In church history, the term acephali (from Ancient Greek: ἀκέφαλοι "headless", singular ἀκέφαλος akephalos from ἀ- a-, "without", and κεφαλή kephalé, "head") has been applied to several sects that supposedly had no leader. E. Cobham Brewer wrote, in Dictionary of Phrase and Fable, that acephalites, "properly means men without a head." Jean Cooper wrote, in Dictionary of Christianity, that it characterizes "various schismatical Christian bodies". Among them were Nestorians who rejected the Council of Ephesus condemnation of Patriarch Nestorius of Constantinople, which deposed Nestorius and declared him a heretic.
Those who refused to acknowledge the authority of the Council of Chalcedon were originally called Haesitantes; the Acephali developed from among them, and, according to Blunt, the earlier name – Haesitantes – seems to have been used for only a short time.
With the apparent purpose of bringing the orthodox and heretics into unity, Patriarch Peter III of Alexandria and Patriarch Acacius of Constantinople had elaborated a new creed in which they expressly condemned both Nestorius and Eutyches, a presbyter and archimandrite, but at the same time rejected the decisions of the Council of Chalcedon. This ambiguous formula, though approved by Byzantine Emperor Zeno and imposed in his Henoticon, could only satisfy the indifferent.