We consider two-dimensional waves in a rectangular container which is periodically excited along its length in the horizontal direction. In general a standing wave of odd mode number whose frequency is close to the forcing frequency is excited. However, we show in this paper that the neighboring even mode, though not directly excited, may be excited through an energy transfer from the odd mode. As a result, the wave response becomes superposition of two standing waves which are not in general in phase with each other. Consequently the mixed-mode wave motion is not standing waves but traveling waves. We employ a perturbation method to derive amplitude equations governing the dynamics of these two modes. Studies of the steady-state solutions and their stability lead to bifurcation diagrams showing the sequences of the events leading to the instability and the parameters for which the standing waves become unstable. ©1998 American Institute of Physics.