  We construct an asymptotic expansion in powers of the coupling constant
directly of the cross-section for pair production and decay of fundamental
unstable particles. The resonant and kinematic singularities arising in the
expansion we treat in the sense of distributions. This mode allows us to
transform formally divergent integrals into absolutely convergent ones with
keeping the asymptotic property of the expansion. The appropriate procedure is
elaborated up to an arbitrary order of the expansion. The peculiarity of
application of the procedure in the threshold region is analysed. The scheme of
the calculations within the NNLO approximation is explicitly discussed.
