Magnetic buoyancy instabilities may be a significant cause of flux loss from the solar interior. This paper extends the linear theory for such instabilities, which has been widely studied, into the weakly non-linear régime to obtain solutions valid for small but finite-amplitude motions. We consider both static and rotating equilibrium states but, for simplicity, focus attention only on the two-dimensional interchange modes. The method used in obtaining the solutions is due to Coullet and Spiegel (1983)—a summary of the method, together with its advantages, is contained in Section 2.