Front propagation is studied in several reaction-diffusion models based on the Oregonator model of the Belousov-Zhabotinsky reaction. Each system involves autocatalysis (X-->2X), termination (2X-->0) and consumption of the autocatalyst (X-->0, X+Y-->0), augmented with interconversion (X<->R) between the autocatalyst X and a rapidly diffusing unreactive species R. We investigate the dependence of the front velocity on the diffusion coefficients of X and R, the interconversion rates, and the other kinetic parameters, when the system possesses either one or two stable steady states.