This article is concerned with a posteriori error estimates for a discrete-fracture, multidimensional, numerical model for flow in a fractured porous medium. Local residual error estimators are defined and upper and lower bounds in terms of these estimators for both the pressure and the Darcy velocity are derived. Numerical examples using these estimates for automatic grid refinement are given. Keywords A posteriori error estimate · mixed finite element · reduced model · fractured porous media.