Abstract: We study a 2×2 system of non-strictly hyperbolic conservation laws arising in three–component gas flooding for enhanced oil recovery. The system is not strictly hyperbolic. In fact, along a curve in the domain one family is linearly degenerate, and along two other curves the system is parabolic degenerate. We construct global solutions for the Riemann problem, utilizing the splitting property of thermo-dynamics from the hydro-dynamics. Front tracking simulations are presented, using the global Riemann Solver.