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A criterion for the investigation of the stability of a certain class of non-linear system with sinusoidal input is proposed. It is derived from the concepts of the describing function method and the circle criterion. If the non-linear system satisfies the restrictions of describing function analysis and if the characteristic of the non-linearity is bound in a sectory/eÂ¿[a, b], there exists a critical region in the G inverse polar plane which contains ail possible describing functions of non-linearities bounded in this sector. Sufficient condition for the stability of the system is assured if the locus of the linear element does not intersect the critical region.