Forced synchronization of selfoscillating system with two degrees of freedom is studied in the case when there are no resonance relations between eigenfrequencies and interaction of the modes has the form of mode competition. Stability conditions for the regimes of one and twofrequency oscillations are obtained analytically. The structure of synchronization tongues on the frequency–amplitude of external driving parameters plane is studied numerically. Mechanisms of establishing of the synchronous regime are considered depending on coefficients of nonlinear mode coupling.
