The survey [1] of results obtained in the study of the conditions for the existence of motion with precession in the dynamics of systems of rigid bodies indicates that in the classical problem concerned with the motion of a rigid body precession of general form occurs [2], the conditions for the existence of which have not been studied in the generalized problem. The present paper fills this gap. A new solution of the generalized problem characterized by the presence of precession of general form is constructed. The case of integrability, which was presented in [2] for the classical problem, is a special case of this solution.
