Invention of syllogism theory is one of the main achievements of Aristotle. Having constructed a theory of simple categorical syllogism, Aristotle laid the foundation for the doctrine of the complex, hypothetical syllogisms (see Analytica Priora 40a 20-41b 5; 45b 11-20; 50a 11 - 50b 2; Topica 112a 16-30; 113b 15 -114a). However, Aristotle never built the doctrine of the complex syllogisms. Theophrastus and Eudemus made attempts to develop the ideas of Aristotle. Simultaneously, the Stoics have created their own “hypothetical syllogistic”. But we heard just fragments of the Peripatetics' and the Stoics' work. According to historians of logic, they are based on the relationship between the proposals, while the syllogistic of Aristotle is built upon the relationship between terms. Alexandre of Aphrodisias, John Philoponus, the Neoplatonic followers of Ammonias, Galen, Sextus Empiricus and the others composed commentaries on Aristotle's teaching on the hypothetical syllogisms. A survived treatise “On the hypothetical syllogism” by Boethius is particularly valuable as one of the few Latin commentaries on Aristotle's logic. Our study demonstrates that neither in Greek nor in Latin commentaries the Stoic syllogistic is opposed to the syllogistic of Aristotle and the Peripatetics. We conclude that that ancient commentaries show not the union but complementary of the Peripatetic and Stoic systems. The ancient logic schools apparently tried to fulfill Aristotle's idea of building a unified theory of the syllogism.