With the analysis of eigenvalues, it is found that a Hopf bifurcation would occur from the steady state of a dissipative three-wave interaction, so long as the contraction rate of its volume in phase space is low enough. The critical value of the contraction rate and the frequencies of the oscillation obtained from the eigenvalues are in good agreement with the results of solving the dynamk equations in the linear stage. It is also shown that no pitchfork bifuraction would occur.