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MATEXP, a general purpose digital computer program, was written for solving systems of ordinary differential equations by the matrix exponential method. MATEXP has several advantages over standard numerical integration routines. It gives virtually exact solutions to constant-coefficient homogeneous ecl_l . . lRti ons and to nonhomogeneous equations for which the forcing functions are constant during the computation interval. The speed at which the equations are solved and the accuracy of the solution are es sentially unaffected either by the degree of cross-coupling of the equations or by whether or not the coefficient matrix is nonRingular or that its eigenvalues are distinct.The method has been extended to nonlinear equations and equations with time-varying coefficients; this use is very effective for engineering systems analysis problems.