Frequency‐jump effects associated with nonlinear mode competition are investigated in an oscillator configuration consisting of a passive linear resonance system coupled to an active nonlinear resonance system. These effects give rise to a hysteresis pattern whose height and width can be related to system parameters such as the resonance frequencies, dissipation, coupling coefficient, etc. It is noted that these effects offer a novel means of determining these parameters in cases in which conventional techniques may not be desirable or as advantageous. The analysis provides a qualitative explanation of empirical observations in a recent nuclear magnetic resonance experiment [R.S. Timsit and J.M. Daniels, Rev. Sci. Instrum. 47, 953 (1976)]. The results also apply to other nonlinear resonance systems such as lasers, microwave generators, and electronic oscillators.