Autocatalytic reaction fronts propagating in a Poiseuille flow present a change of speed and curvature depending on the strength of the flow and on the direction of front propagation. These chemical fronts separate reacted and unreacted fluids of different densities, consequently convection will always be present due to the horizontal density gradient of the curved front. In this paper, we find the change of speed caused by gravity for fronts propagating in vertical tubes under a Poiseuille flow. For small density differences, we find axisymmetric fronts. Our theory predicts a transition to nonaxisymmetric fronts as the distance between the walls is increased. The transition depends on the average speed of the Poiseuille flow. © 2007 The American Physical Society.