A microscopic approach to the description of multisublattice magnets with strong exchange interaction is proposed. Low-frequency dynamics of such magnets is characterized by the appearance of an additional dynamical variable, i.e., the orthogonal matrix of rotation, which corresponds to the total breaking of spin invariance [brokenSO(3)symmetry]. The structure of the source that breaks the symmetry of the equilibrium Gibbs distribution is established. The quasiaverage representation is generalized to weakly anisotropic, locally equilibrium states. The thermodynamics of such states is constructed. The method of reduced description is formulated and in its framework the hydrodynamic equations for the density of total spin and the matrix of rotation are obtained. The spectra of spin waves are found and the number of Goldstone and activation modes is determined. Two-sublattice ferrimagnet is considered as a special case of the magnet with brokenSO(3)symmetry, which corresponds to the special dependence of thermodynamic functions from the matrix of rotation. ©1997 American Institute of Physics.