[en] The analysis of stability of various circuits ensuring the synchronization of acceleration cycle frequency with the supply line frequency and formation of magnetic field plateau for fast cyclic acelerators is carried out. The base of all methods of synchronization is discrete variation of the equivalent frequency of the resonance contour in the function of difference of supply line periods and eigen frequency of the resonance contour. The analysis has shown that for real parameters of accelerator supply systems the stability conditions can be always realized. The nonlinear dependence of trying out of control effect limits (but slightly) the synchronization zone width and under proper construction of synchronization facility does not deteriorate qualitative characteristics of the system. Therefore the basic criterion at the choice of synchronization scheme variant is ensuring of required technical and economic indices