The article deals with the problem of monoaxial stabilization of an angular position of a rigid body exposed to a nonstationary perturbing torque. The perturbing torque is represented as a linear combination of homogeneous functions with variable coefficients. It is assumed that the order of homogeneity of the perturbations does not exceed the order of homogeneity of the restoring torque, and the variable coefficients in the components of the disturbing torque have zero mean values. A theorem on sufficient conditions for the asymptotic stability of a programmed motion of the body is proven with the use of the Lyapunov direct method. The found conditions guaranteeing the solution of the problem of monoaxial stabilization of the body do not impose any restrictions on the amplitudes of the oscillations of the disturbance torque coefficients. The results of numerical modeling, illustrating the conclusions obtained in the work, are presented.