<p>In this study, we investigate the control of the mechanical system consisting of two rigid spherical bodies rolling over each other in the gravity field. The spherical body (spherical shell or sphere) with the larger radius rolls without slipping and separation along the horizontal plane. The sphere of the smaller radius rolls without slipping and separation on the outer or inner surface of the spherical body of the larger radius. By controlling the translational motion of the ground (reference) plane, we ensure that the sphere of the smaller radius moves according to a given law. This problem is the nonholonomic problem with servo-constraints. We also investigate the stability problem of the particular solution of equations of motion. To do this, we use approach based on using the equations in variations. The stability problem is investigated in the following cases. The small sphere is located at the top point on the outer surface of the spherical shell. The small sphere is located at the lower point of the inner surface of the spherical shell. The small sphere rolls along a circle defined on the outer and inner surfaces of the spherical shell.</p>