The purpose of the project was the development of an accurate method for solving the complete equations of dissociated laminar-boundary layer flow of a binary gas in chemical nonequilibrium. The primary concern was the mathematical solution rather than the physics and chemistry of the flow processes. The method of solution consists of replacing the partial derivatives with respect to the flow direction by finite differences, while retaining the derivatives in a direction normal to the boundary, so that the partial differential equations become approximated by ordinary differential equations. The ordinary differential equations are solved simultaneously at a given station in the flow direction as the calculation proceeds downstream. The method was programmed for an IBM 7094 computer for the special case of air treated as a single gas, and solutions for a variety of flows are presented. Results are shown for nonsimilar flows at velocities up to Mach 25 for various wall temperatures and amounts of dissociation. Effects of chemical-reaction rates, wall catalyticity, and various fluid-property relations are shown.