The equations for the turbulent mixing of a two-dimensional supersonic jet issuing into an ambient supersonic stream are formulated. Both streams consist of a mixture of chemically active and possibly reacting gases, therefore any release by chemical reaction is included; the net mass rate of production of species is obtained on the assumption that the reaction rate constant is given by an expression reducible to the classical Arrhenius law. The equations first given in terms of the x, and y coordinates, are expressed in dimensionless form and in terms of the % and \p coordinates, where \p is the stream function. The resulting expressions are all of the heat conduction type; they are put in a finite difference form by using the Crank-Nicolson method of substituting finite difference approximations for both the t ime and space derivatives. The mixture is assumed to consist of six species, namely H 20. H2, 02 , C02 , CO, and N2, and the oxidation of H2 and CO is assumed to take place according to a single-step chemical reaction. The solution of the problem is based on the simultaneous solution of 87V linear algebraic equations in 8N unknowns, N being the number of internal grid points at every step in the ^-direction, and 8 the total number of unknowns at each grid point, namely velocity, temperature, and concentration for each of the six species. A method of obtaining initial and boundary conditions from available in viscid jet flow solutions is discussed. The equations are programed for calculation on an IBM-704 computer. Finally, one typical case is considered, and plots of velocity, temperature, and concentration profiles are given for he initial stages of development of the mixing layer.