Abstract. Criteria for the Lyapunov stability of solutions to systems of ordinary differential equations are presented in the difference, additive, and integral forms. They contain the necessary and sufficient conditions and do not transform the functions in the right-hand side of the system. In general, the criteria are intended for computer implementation, and some of them for the analytical research. Based on the comparison of the integrands, the stability of some systems of nonlinear equations is analyzed without a priori solutions. The programmed criteria are given for general systems, examples and results of program and numerical experiments are presented.

Keywords: Lyapunov stability analysis, approximate solution of ordinary differential equations, recurrent transformations of difference solutions, numerical modeling of stability, indications of stability of linear and nonlinear systems, computer analysis of stability.