This study details the derivation and application of an approximate Riemann solver of the Roe type specifically designed for the numerical simulation of inviscid and viscous flow problems involving general and virtually arbitrary mixtures of thermally perfect gases in local chemical equilibrium. The solution procedure is by no means limited to airflows and will be applied to an oxygen/hydrogen mixture as well. A “black box” solver for the local equilibrium composition of a gas mixture of known density and internal energy is coupled with the flow solver, which is based on the newly derived flux-difference-split technique. A few test cases, including both external and internal flows, illustrate the capabilities and the overall efficiency of the flow solver. © 1994 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.