The review examines the dynamics of a special class of magnetic substances (magnetically ordered crystals) in which the magnetic atoms do not coincide with the symmetry center (provided that such a center exists in the crystal). Research into the magnetoelectric and antiferroelectric interactions in such magnets has led to a new section in the spin dynamics of both the electrical and nuclear subsystems. The review is based primarily on the latest works (2001-2004) done by theoretical physicists from the Ural region. Several results of the pioneering works (1988-1990) of Ukrainian physicists, who opened this new section in spin dynamics, are also discussed. All this research has made it possible to compare the predicted effects for different crystal systems and thus has provided a more meaningful arrangement of the desired experiments.