The dynamics of dual-spin spacecraft under effects of energy dissipation are considered in this paper, where the damper masses in the platform (P) and the rotor (R) cause energy loss in the system. Following Mingori,1 the Floquet theory is employed to obtain stability charts for different relative spin rates of Rwith respect to P. Based on the general model for the system with two nutation dampers, models are presented for a system whose nutation damper exists only in the platform as well as a system without nutation damper. The results obtained from the Floquet theory agree with the energy sink analysis in the literature. The investigations show that for spacecraft with less than two nutation dampers there is no need to apply Floquet theory, and the Routh-Hurwitz criteria provides necessary and suffcient conditions for stability. Furthermore, for the system with less than two nutation dampers, the Lyapunov stability criteria agrees with Routh-Hurwitz criteria.