  The paper is devoted to further development of the new approach in
equilibrium statistical mechanics the basis of which was worked out in a series
of articles by the author. The approach proceeds on the use of a hierarchy of
equations for reduced density matrices in the case of thermodynamic
equilibrium. The present paper deals with a system containing particles of
several kinds with arbitrary spin, for which the hierarchy obtained previously
for a single-component system is generalized. Thermodynamics of the
multicomponent system described by the hierarchy deduced is constructed as
well.
