  The analytization procedure which allows one to remove nonphysical
singularities of the QCD running coupling constant $\bar\alpha_s(q^2)$ in the
infrared region is applied to standard as well as to iterative solutions of the
two-loop renormalization group equation. Non-leading at large momentum
nonperturbative contributions in $\bar\alpha_s(q^2)$ are obtained in an
explicit form. The coefficients of nonperturbative contributions expansions in
inverse powers of the squared Euclidean momentum are calculated. For both cases
considered there appear convergent at $q^2>\Lambda^2$ power series of negative
terms with different dependence on term numbers.
