Predicting the fate of chlorinated ethenes in groundwater requires the solution of equations that describe both the transport and the biodegradation of the contaminants. Here, we present a model that accounts for (1) transport of chlorinated ethenes in flowing groundwater, (2) mass transfer of contaminants between mobile groundwater and stationary biofilms, and (3) diffusion and biodegradation within the biofilms. Equations for biodegradation kinetics account for biomass growth within the biofilms, the effect of hydrogen on dechlorination, and competitive inhibition between vinyl chloride and cis-dichloroethene. The overall model consists of coupled, non-linear, partial differential equations; solution of such a model is challenging and requires innovative numerical algorithms. We developed and tested two new numerical algorithms to solve the equations in the model; these are called system splitting with operator splitting (SSOS) and system splitting with Picard iteration (SSPI). We discuss the conditions under which one of these algorithms is superior to the other. The contributions of this paper are as follows: first, we believe that the mathematical model presented here is the first transport model that also accounts for diffusion and non-linear biodegradation of chlorinated ethenes in biofilms; second, the SSOS and SSPI are new computational algorithms developed specifically for problems of transport, mass transfer, and non-linear reaction; third, we have identified which of the two new algorithms is computationally more efficient for the case of chlorinated ethenes; and finally, we applied the model to compare the biodegradation behavior under diffusion-limited, metabolism-limited, and hydrogen-limited (donor-limited) conditions.