Propagating reaction-diffusion fronts in a two-variable chemical system, the so-called open unstirred cubic autocatalator, are analyzed. Both situations of stable/metastable and stable/unstable connections are considered. Numerical results for the front velocities and profiles are supplemented with analytical calculations either exact or obtained perturbatively. Special emphasis is devoted to the question of velocity selection. In this respect, abundant use is made of the marginal stability criteria, either in their linear or nonlinear formulations. Finally, some peculiar phenomenologies related to the appearance of double fronts are examined. (C) 1997 American Institute of Physics.