The dynamics of dual-spin spacecraft which containing a proposed nutation damper which consisting of a ring totally filled with a viscous liquid with offset center, to improve damping, is investigated. The equations of motion were developed using Newton-Lagrange approach resulting equations in terms of spacecraft's and damper's parameters, which are given in dimensionless form. The expression of the nutation angle and time constant in both modes are developed using zero-order approximation technique. The equilibria states and stability condition, and the analytical expression for residual nutation angle were derived. The analytical results were compared with those found numerically using computer simulation program named MATLAB, ver. 7. Also the effect of various spacecraft's and damper's parameters on the dynamic and damping characteristics are discussed. The three dimensional graphical representation. of the first and the second relative equilibria states are introduced. The numerical results are compared with the analytical for both modes of motion, where the percentage error of the time constant for nutation mode is less than (3.6%), and for spin mode is less than (8%). As an important result its concluded that the proposed damper works better than that used by Alfriend