Based on the Bogolyubov chain and a new approximation of the two-particle distribution function a new system of equations of correlation magnetodynamics is obtained for antiferro- and ferrimagnets. Body-centered and face-centered crystal lattices are considered. The system contains one world-magnetic equation of the Landau-Lifshitz-Bloch type for each sublattice and several equations for pairwise correlations between sublattices. In this case, the main difficulty is the calculation of the integral coefficients of the resulting system of equations.