The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is an elliptic equation for the pressure and the other is parabolic equation for the concentration of one of the fluids. Since the pressure appears in the concentration only through its velocity field, we choose a mixed finite element to approximate the pressure equation and for the concentration we use the standard Galerkin method. We shall obtain an explicit a posteriori error estimator in L2 (L2) for the semi-discrete scheme applied to the nonlinear coupled system.