For describing the pair correlations of the electrons in the many- electron systems a new method of reducing the many-particle problem to the two- particle problem is developed. Instead of the wave function, one- and twoparticle density matrices are used. In the process of deriving an equation for the two-particle wave function, which describes a pair of electrons in the field of the others, a transition to the second quantization representation is accomplished. The solution of the obtained equation is carried out with the help of perturbation theory. (auth)