[en] A study is made of the nonrelativistic approximation in the two-body problem, with an interaction through a non-Abelian gauge field for the case of the SU(2) group. It is shown that the problem can be reduced to the solution of a system of quasilinear equations of elliptic type. The properties of the regular solutions are given. The behavior of the quark fields of the sources is considered in the self-consistent field which is found. The results of numerical calculations are discussed. The two-body problem is analyzed on the basis of the resulting exact solutions. 21 refs., 8 figs