An integral method is developed in order to solve approximately the governing equations for a multitemperature, nonequilibrium ionizing, compressible boundary layer. This method is based on classical momentum and energy integral methods which are used in conjunction with the Howarth–Dorodnitsyn transformation. A novel feature of this method is the separate treatment of the translational or sensible energy equations for each species. As an illustrative example, this method is applied to the problem of a shock-generated ionizing argon boundary layer on a flat surface at a uniform temperature. Reasonable agreement for this case is found between this approximate theory and existing experimental and numerical results.