A new asymptotic stability criterion for non -

| A new suucient condition for asymptotic stability of ordinary diierential equations is proposed. Unlike classical Liapunov theory, the time derivative along solutions of the Liapunov function may have positive and negative values. The classical Liapunov approach may be regarded as an innnitesimal version of the present theorem. Veriication in practical problems is harder than in the classical case; an example is included in order to indicate how the present theorem may be applied.