The method of multiple scales, in both space and time, is used to derive a set of three nonlinear coupled partial differential equations which model the evolution of a train of capillary-gravity waves contained in a channel of finite depth and which arise from the resonant interaction of the Nth and (N + l)th harmonics of the fundamental mode. These equations are used to investigate the stability of the waves to plane-wave perturbations, which may be longitudinal, transverse or oblique to the direction of the propagation of the waves.