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.(p180)
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.
The term applied to a 5th-century faction among the Eutychians, who seceded from Peter, a Monophysite or more accurately a Miaphysite, in 482, after Peter signed the Henoticon and was recognised by Zeno as the legitimate patriarch of Alexandria by which they were "deprived of their head". The condemnation of Eutyches irritated the rigid Monophysites; the equivocal attitude taken towards the Council of Chalcedon appeared to them insufficient, and many of them, especially the monks, deserted Peter, preferring to be without a head, rather than remain in communion with him. Later, they joined the adherents of the non-Chalcedonian Patriarch Severus of Antioch. They were, according to Oxford English Dictionary Online, a "group of extreme Monophysites" and "were absorbed by the Jacobites".
Liberatus of Carthage wrote, in Breviarium causae Nestorianorum et Eutychianorum, that those at the Council of Ephesus who followed neither Patriarch Cyril I of Alexandria nor Patriarch John I of Antioch were called Acephali.
Esaianites were one of the sects into which the Alexandrian Acephali separated at the end of the 5th century. They were the followers of Esaias, a deacon of Palestine, who claimed to have been consecrated to the episcopal office by the Bishop Eusebius. His opponents averred that after the bishop's death his hands had been laid upon the head of Esaias by some of his friends.(p148)