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The statistical theory of the nuclear magnetic relaxation of the spins in a rotating frame has been developed by the theoretical functional method of projecting operators (PO). This method of PO was used for finding the kinetic equation for the spin TCF. A general expression for the relaxation rates in the case of slow-and fafit thermal motion in the spirit of the well known Kubo-Tomita theory is determined from the structure of these kinetic equations. mTa cTaTucTwecIiaH Teopm Hnepaofi MarHmHofi peaaKcauue C~M H O B BO spawarn-uIeiicn cucTeMe KoopnuHaT B cnysae I I~O M~B O~L H~I X M~X~I I~M O B pena~ca1~Iiu.