The structure of red giant stars allows non-radial oscillation modes which propagate as p-modes near the surface, to propagate below the convection zone as g-modes with very high radial wave number [Dziembowski (1971, 1977), Shibahashi and Osaki (1976)]. Under some conditions the oscillations in these two propagation regions can be treated as virtually independent normal modes [Shibahashi and Osaki (1976)]. This paper examines the situation in which this approximation is not good, and discusses possible observational consequences of the interaction of the two propagation regions.The linearized differential equations describing non-radial adiabatic oscillations in stars can be written in the form, 1a1b