[en] A systematic analysis of the influence of the magnetic centers, strongly coupled with a lattice, on the spin-lattice relaxation (SLR) of the other centers, weakly coupled with a lattice, is carried out. It is shown that the different mechanisms provide the different dependences of relaxation probabilities upon the temperature and concentration. The type of such dependences has been determined for a number of mechanisms. A comparative analysis of the theory and the experiment has been performed and the explanation of some experimental results previously considered to be anomal has been given. It is pointed out that there is a possibility to judge about the nature of magnetic center interactions considering their characteristics of the SLR