In the present work, asymptotic methods are used to derive new expressions for the law of the wall, for the law of the wake and for the skin-friction and the Stanton number equations, for compressible turbulent boundary layers with heat and mass transfer. The results are compared with previous theories and experiments showing good agreement. The two parameters in the law of the wall, the angular coefficient and the linear coefficient of the straight part of the velocity and the temperature profiles plotted in appropriate logarithmic coordinates, are shown to vary with Mach number. Only the second of these parameters, the linear coefficient of the straight line, is shown to vary with the injection rate. No dependence of these parameters on Eckert number, E could be assessed. Also, it emerges from the present analysis that the dissipation effects become important only when E = 0(u(tau)(-1)), u(tau) = non-dimensional friction velocity.