AbstractThe most popular method of investigation of periodic oscillations in nonlinear systems is the describing function method. Two theorems on the existence of a free vibration in a given neighbourhood of the approximate vibration obtained by this method are presented in the paper. Moreover, for a typical transfer functionK(jω) of the linear part of the system and a typical describing function of the non‐linear element, the theorem on the estimation of frequency of the free vibration is giv