Abstract A Hamiltonian system with coupled two dibberent kinds of modes is studied. When the coupling vanishes, one kind of modes is nonlinear oscillators, describing coherent three-wave interaction and consisting an integrable Hamiltonian. Another kind of modes is constants of motion. In the first order of approximation, resonance occurs due to the coupling between these two kinds of modes. The resonace condition is relevant to the existing linear brequencies and their mismatch as well as the harmonic frequencies of the nonlinear variations of the amplitudes of the oscillators.