In the nonlinear drift-waves driven by a sinucoidal wave, with variations of the driving frequency and strength, crossing and ‘avoided crossing' may appear between the nonlinear complex eigenvalues of a negative-energy mode and a positive-energy mode. While the ‘avoided crossing' occurs, the positions of these two modes are somehow exchanged. Such nonlinear resonance is related to the Hopf bifurcation in weak dissipations.