Rule of St Basil

Basilian monks are monks who follow the rule of Saint Basil the Great, bishop of Caesarea (330–379). The monastic rules and institutes of St. Basil are important because their reconstruction of monastic life remains the basis for most Eastern Orthodox and some Greek Catholic monasticism. Saint Benedict of Nursia, who fulfilled much the same function in the West, took his Regula Benedicti from the writings of St. Basil and other earlier church fathers. In the Eastern Orthodox Church, monks do not generally call themselves "Basilians", while the Greek Catholics do. Thus the expression "Basilian monk" almost always refers to religious of those Eastern Catholic Churches which follow the Byzantine Rite.

Under the name of Basilians are included all the religious that follow the Rules of St. Basil. It should be noted that the "Rules" of St. Basil are not intended to be constitutions like the various Western monastic Rules; rather, it is a collection of his responses to questions about the ascetic life—hence the more accurate original name: Asketikon. There were two such collections, the Greater Asketikon and the Lesser Asketicon (the difference between the two being their length).

Eastern monasticism has never possessed the hierarchical organization which ordinarily constitutes the Western religious orders, properly so called. Only a few houses were formerly grouped into congregations or are today so combined. Usually each monastery follows its own traditions, and is either under the local bishop or is "stavropegial" (directly under the Patriarch or a Synod of bishops).

...
Wikipedia