In this paper we develop an approximation scheme for solving a coupled system of flow and contaminant transport with adsorption in unsaturated-saturated porous media. The flow model is based on nonlinear Richard's equation and is coupled with the transport equation through saturation and Darcy's velocity (discharge) terms. The approximation is based on time stepping, operator splitting and the method of characteristics (see Pironneau (Numer. Math. 38 (1982) 309), Douglas and Russel (SIAM J. Numer. Anal. 19(5) (1982) 871)). The nonlinear terms in Richard's equation are approximated by means of a relaxation scheme (see Jager and Kacur (Math. Modelling Numer. Anal. 29 (1995) 605), Kacur (IMA J. Numer. Anal. 19 (1999b) 119), Kacur (SIAM J. Numer. Anal. 36(1) (1999a) 290)). The convergence of the approximation scheme is proved. Some numerical experiments in ID are included. (C) 2003 Elsevier Ltd. All rights reserved.