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The attitude stability of a dual-spin satellite containing energy disipators on both bodies is investigated. Following Mingori, a symmetrical configuration of the satellite with a mass-spring-dashpot damper on each part is considered, and some new stability results are derived by the application of the Routh-Hurwitz criterion. lt is indicated that the Routh-Hurwitz criterion gives only sufficient conditions of stability for the dual-spin satellite considered. A criterion which is believed to represent both the necessary and sufficient condition of stability is presented here and this is used to check the stability of two specific designs of the dual-spin satellite.