Spin-axis stabilisation of spacecraft is a problem of partial stabilisation for non-linear dynamical systems. In this article the analysis of spin-axis stabilisation of underactuated rigid spacecraft in the presence of sinusoidal disturbances is presented. By using the Euler-Poisson form to describe the equations of motion and assuming the disturbances in three axes are decoupled with known frequencies, the paper first studies the problem of the underactuated rigid axisymmetric spacecraft by applying the internal modal principle to eliminate the sinusoidal disturbance. Then the paper turns to the more complicated asymmetric spacecraft, where the boundedness of the angular velocity for the underactuated axis is analysed in detail. The paper also proves the global asymptotic stability of the closed-loop systems for both axisymmetric spacecraft and asymmetric spacecraft by combining the Lyapunov direct method with the LaSalle's theorem. The simulation results show that the proposed control law is effective in the presence of sinusoidal disturbance.