Hamiltonian approach to the low-frequency dynamics of manysublattice magnets has been developed. The Poisson brackets for dynamical variables are derived from variational principle proceeding from transformations that leave invariant the kinematic part of the action. Nonintegral terms of the action variation are interpreted as generators of these transformations. Magnetic systems with totally broken symmetry with respect to spin rotations and antiferromagnetics are considered. Hydrodynamical asymptotics of Green functions are found. In the case of description of magnet on the base of Landau-Lifshits equations it is shown how the reduction does occur from complete set of variables (sublattice spins) to the short description variables (rotation matrix and density of total spin).