  In the framework of analytic approach to QCD the nonperturbative
contributions in running coupling of strong interaction up to 4-loop order are
obtained in an explicit form. For all $Q>\Lambda$ they are shown to be
represented in the form of an expansion in inverse powers of Euclidean momentum
squared. The expansion coefficients are calculated for different numbers of
active quark flavors $n_f$ and for different number of loops taken into
account. On basis of the stated expansion the effective method for precise
calculation of the analytic running coupling can be developed.
