Techniques of numerical bifurcation theory are used to study stationary and periodic solutions of an intermediate coupled model for tropical ocean-atmosphere interaction. The qualitative dynamical behavior is determined for a volume in parameter space spanned by the atmospheric damping length, the coupling parameter, the surface layer feedback strength and the relative adjustment time coefficient. The study shows how this behaviour arises in parameter space through the interaction of the different branches of equilibrium solutions and the singularities on these branches.