The stability of the Kippenhan-Schluter model prominence to ideal MHD perturbations is analyzed. It is shown that all modes with g⋅∇v1=0, where g is the gravitational field and v1 the perturbed velocity, are stable. The analysis is done by self-consistently taking into account the spatial variation of equilibrium quantities (density, magnetic field) and looking for bounded eigenmodes. Some consequences (of the derived stability of perturbations) are drawn with regards to observed prominence phenomena.