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It has been known for a considerable time that non-linear systems may exhibit multivalued response under external periodic excitation. The stability of these forced oscillations has been extensively investigated for second-order systems and a general criterion for their stability was found. Stability of higher order systems was investigated by means of the incremental describing function. This function must be calculated for every case of interest. In this paper the general criterion formerly derived for second-order systems is extended to higher order systems. Thus it is not necessary to make a special stability investigation in every case.