A chemical front propagating upward in a fluid separates heavy unreacted fluid from light reacted fluid. The density difference caused by the front propagation leads to convection. Convection enhances the front speed and curves the front as it propagates upward in a tube. The convective front propagates with constant speed and is steady in a frame of reference comoving with the front. This paper presents a linear stability analysis of the convective front. The fronts are modeled using a front evolution equation coupled to Darcy’s law for flow in porous media and the Navier-Stokes for viscous flow. The solutions can be either axisymmetric or nonaxisymmetric as observed in experiments in tubes. For flow in porous media, there is a region of bistability between both types, whereas in viscous flow the axisymmetric front is always unstable. © 1997 The American Physical Society.