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We explore some properties of twin kilohertz quasiperiodic oscillations (QPOs) in a simple toy-model consisting of two oscillation modes coupled by a general nonlinear force. We examine resonant effects by slowly varying the values of the tunable, and nearly commensurable, eigenfrequencies. The behavior of the actual oscillation frequencies and amplitudes during a slow transition through the 3:2 resonance is examined in detail and it is shown that both are significantly affected by the nonlinearities inthe governing equations. In particular, the amplitudes of oscillations reflect a resonant exchange of energy between the modes, as a result the initially weaker mode may become dominant after the transition.