The terminological system of the museum affair is the part of vocabulary, which includes the concepts denoting the names of the objects, actions, processes, phenomena, etc. related to museums. It is combined with the relevant sciences and spheres of the life - arts, biology, geography, history, as well as with archeology, vexillology, heraldry, numismatics, faleristics, architecture, sculpture, painting, library affairs, etc. One of the main sources for the formation of the modern Ukrainian terminological system of the museum affair is the foreign language terms borrowing. The terms that were borrowed from a classical languages, in particular from Greek, occupy a special place in the Ukrainian terminology system of museum science, along with specific terms. Here we paid a special attention to Greek borrowing terms as an important way to replenish the terminological dictionary. Also, the composition of the borrowings and specifics of the operation by types of the foreign language terminology were determined. The role of the Greek prepositional and postpositional components of the terminological system of the museum affair was described. The functioning of the Greek borrowing, as a mean of the naming of scientific concepts, reflected a natural process of language development. Borrowings from the Greek play not only a positive role in the formation of the vocabulary, but also firmly established and form an integral part of the terminological system for several centuries of its functioning.