The non-relativistic current algebra approach is analyzed subject to its application to studying the distribution functions of many-particle systems at the temperature equilibrium and their stability properties.We show that the classical Bogolubov generating functional method is a very effective tool for constructing the irreducible current algebra representations and the corresponding different generalized measure expansions including collective variables transform.The effective Hamiltonian operator construction and its spectrum peculiarities subject to the stability of equilibrium many-particle systems are discussed.