We derive a set of nonlinear equations for magnetogravity waves based on a reduced set of fluid variables. The equations describe the self-consistent time evolution of the density perturbation and the velocity and magnetic vector potential component in the direction along the horizontal background magnetic field. These reduced equations take account of the propagation of Alfv¿n waves along the background field, of gravity waves perpendicular to the background field and their mutual nonlinear interaction. The Strauss-Boussinesq approximations are shown to be applicable if the vertical gravitational scale height H is much larger than the typical vertical wavelength &lgr;z under consideration and if the aspect ratio of the fluctuation wavelengths parallel to the background magnetic field to the perpendicular wavelengths is even larger than H0/&lgr;z. As an application of these equations, we investigate some typical nonlinear phenomena. A stability analysis of plane harmonic waves suggests that as a result of the parametric decay instability the energy of buoyancy fluctuations is eventually converted into magnetic fluctuation energy of Alfv¿n waves with large vertical wave number. Furthermore it is shown that modonlike, horizontally extended traveling vortices are a nontrivial solution to the Boussinesq-Strauss equations. The vortex axis of these modons is inclined with respect to the background magnetic field and in a stably stratified plasma, a necessary condition for the existence of these solutions is an apparent phase velocity along the background magnetic field smaller than the Alfv¿n velocity. ¿ American Geophysical Union 1993