We study the behavior of solute fronts for an in situ bioremediation scenario in which a sorbing substrate is degraded by indigenous microorganisms in the presence of an injected nonsorbing electron acceptor. The fronts behave as traveling waves, which leads to a simple theoretical derivation of the long-term degradation rate of the organic pollutant (substrate). The long-term degradation rate is dependent upon input and background solute concentrations, the flow velocity, and the sorption and stoichiometric coefficients, but it does not depend upon dispersion and microbial kinetic parameters. Numerical simulations show that the analytical method is valid for predicting the long-term degradation rate, although the front velocity and shape exhibit oscillatory behavior under some conditions. Numerical simulations also show that traveling wave conditions are established only after an initial phase in which substrate degradation is strongly dependent upon microbial kinetic parameters.¿ 1997 American Geophysical Union