In this paper the ignition and structure of a reacting compressible mixing layer lying between two streams of reactants with different free-stream speeds and temperatures using finite rate chemistry are considered. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. In particular, for sufficiently large Zeldovich number, the three regimes first described by Linan and Crespo [Combust. Sci. Technol. 14, 95 (1976)]; i.e., ignition, deflagration, and diffusion flame, occur in supersonic as well as in subsonic flows. An analysis of both the ignition and diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows an analysis of the behavior of these regimes as a function of the parameters of the problem. For the ignition regime, a well-defined ignition point will always exist provided the adiabatic flame temperature is greater than either free-stream temperature. For the diffusion flame regime, the location of the flame changes significantly with changes in the equivalence ratio and the Schmidt numbers.