One of the principal drawbacks associated with the use of equations of Koretweg-deVries (KdV) or Kadomtsev-Petviashvili (K-P) form to model wave propagation in a varying channel is the implicit neglect of reflection in those equations. This study formulates pairs of KdV or K-P equations which are coupled through inhomogeneity in bottom slope or channel width, and applies these equations to several propagation problems involving aperiodic and periodic wave motion. The formulation eliminates the neglect of reflection effects in the single KdV or K-P equation approach. Forms of the KdV equations are given which totally account for mass flux balance between the incident and reflected wave. We then examine several cases involving waves propagating in variable channels and compare model results to previously available data. ¿ American Geophysical Union 1988