Summary: We study a system of reaction-diffusion equations containing Monod kinetics which is coupled with a set of ordinary differential equations in Banach spaces. The model includes biodegradation for the time evolution of concentrations of contaminants, nutrient, bacteria, and sorption isotherms both for equilibrium and for nonequilibrium sorption. In order to prove the global existence of a strong solution of this system, we use the fixed point theorem of Leray-Schauder.