General expressions are derived for the critical wave numbers for two-
and three-species reaction mechanisms when their homogeneous steady s
tates are destabilized by a relative flow of at least one species. Ana
lysis of a model of the oscillating peroxidase-oxidase reaction indica
tes that the reaction exhibits this kind of instability. Computer simu
lations of the reaction-flow-diffusion equations generate traveling co
ncentration waves under appropriate conditions.