  We present the O(alpha_s) corrections to the cross section for the reaction
e+e- --> gamma^* --> Q \bar Q in the energy region close to the threshold. We
assume that the energy of the reaction is such that both the perturbative
expansion in the strong coupling constant and expansion in the relative
velocity of the heavy quarks can be used. We explicitly obtain terms
O(alpha_s^2/beta^2, alpha_s^2/beta, alpha_s^2) in the relative correction to
the threshold cross section. Using the ideas of asymptotic expansions, we
demonstrate how an expansion of Feynman diagrams in the threshold region is
constructed. From this analysis we obtain a matching relation between the
vector current in full QCD and the quark-antiquark current in NRQCD at leading
order in 1/m and the second order in the strong coupling constant.
