Abstract: A streamline-multiscale method for numerical simulation of two-phase flow in strongly heterogeneous porous media will be presented. The mathematical model consists of a variable coefficient Poisson equation for pressure/velocity and a continuity equation for water-saturation. First, a multiscale mixed finite-element discretization of the pressure/velocity equation will be presented. A two-scale approach is considered, where basis functions are computed locally (numerically) on a coarse grid to correctly and accurately account for coefficient variations from an underlying fine grid. Second, a coordinate transformation reducing the three-dimensional saturation equation to a one-dimensional equation along streamlines is presented. At the end an application to petroleum engineering, demonstrating the efficiency of the approach with respect to computation time, will be presented (if time permits).