The article presents the main stages in the formation of the Cuman hypothesis of the origin of the Gagauz. Obviously, this version has its strengths and weaknesses. The historical and archaeological data are justified, according to which the population of Dobruja was made up of Turkic-speaking Cumans. The weak side of the hypothesis is that the Cuman language belongs to the Kipchak group, and the Gagauz language belongs to the Oghuz group. However, a number of researchers have tried to give well-founded explanations. Their essence is as follows. The population of Dobruja (Dobrudzhan despotism) before the Ottoman domination spoke the Turkic (Kipchak) dialect. After the conquest of the Balkan Peninsula by the Ottomans, the language of the Ottomans, related to the Cuman dialect, became dominant in the region. At the same time, the Kuman dialect was absorbed by the Ottoman language, which belongs to the Oguz group. These processes, which continued for four centuries, predetermined the Oguz character of the Gagauz language. It should be emphasized that research in this direction needs to be continued. The implementation of research in the field of linguistics, namely the search for Kypchakisms in the Gagauz language, will make significant progress in resolving this important issue for Gagauz studies.