A two-layer shallow water equation model is used to investigate the linear stability of a coastal upwelling front. The model features a surface front parallel to a coastal boundary and bottom topography which is an arbitrary function of the cross-shelf coordinate. Global conservation statements for energy, momentum and potential vorticity are examined to help elucidate the instability mechanism. By combining these conservation statements, a general stability theorem is established which allows the a priori determination of the stability of a coastal upwelling front. The necessary conditions for instability derived for these ageostropic flows differ from a traditional quasi-geostrophic criteria. The stability theorem suggests that a coastal upwelling front may be unstable no matter what the basic state flow configuration is. Confirmation of the existence of these unstable waves, a description of their characteristics and a comparison of their properties to observations are presented in a companion paper. ¿ American Geophysical Union 1989