The attitude stability of a dual-spin spacecraft on a stable stationary orbit around an asteroid subjected to gravity gradient torque is studied in this paper, in which the effect of the second order and degree harmonics C and C of the gravity field of the asteroid is involved. Under some reasonable assumptions, the linearized equations of attitude motion of the dual-spin spacecraft with a nutation damper are presented. Then the necessary and sufficient conditions of attitude stability of the dual-spin spacecraft with a nutation damper are derived. Meantime, the linearized equations of attitude motion and the conditions of attitude stability of the dual-spin spacecraft without a nutation damper are also presented. These results are generalized and encompass a series of special cases, and from which some useful conclusions on the attitude stability of the dual-spin spacecraft are obtained. Examples are given to illustrate the application of these conditions of attitude stability. [ABSTRACT FROM AUTHOR]