Subsurface flow constructed wetlands are one of the different types of wastew- ater treatments used nowadays. There, water is treated by physical, biological and chem- ical processes while flowing through a porous media. Many aspects of detailed processes which take place there are not well-known. In fact, a key point of their behavior is that simultaneously aerobic and anaerobic conditions take place in different parts of the do- main. Mathematically the problem is a Convection – Diffusion – Reaction system of equations, highly coupled because of the nonlinear reaction term that models the biochem- ical processes. An stabilized Galerkin formulation is used for spatial discretization, and the Runge-Kutta-Fehlberg 4-5 scheme is used for time integration. Homogeneous exam- ples with and without oxygen entrance throughout all domain have been used to check the numerical performance of the approach. The Activated Sludge Model No.1 (ASM1) and a six–equations model based on it are used as examples of complex reaction models. Two dimensional examples with oxygen entrance in just part of the domain have been also computed. It has been check that under horizontal low–velocity conditions a discontinuity in oxygen vertical profile is found, even if continuous transition in oxygen entrance is imposed. In this situation, classical convection stabilization has shown to be usefulness to smooth discontinuities produced by source terms. Further numerical improvements needed are indicated, as well as an extension to more realistic biochemical models for subsurface flow constructed wetlands

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