Wolf-Rayet stars may have evolved from massive close binary systems, as a result of the mass transfer processes in such systems. A substantial fraction of all WR stars known is, indeed, found in close binaries, with massive early-type companions. After the outer layers of the initial primary have been removed during Roche Lobe Over-Flow, the remaining stellar core may be a helium-burning helium star, classified observation ally as a WR star. The fraction of such evolved binaries among main-sequence stars can be computed, following recipes from stellar- and galactic evolution and assuming steady, standard-IMF star formation over the last ∼ 109 yr in our Galaxy. Combining these results with the stellar PMF yields the total galactic number of such objects, or alternatively the number expected within, e.g., 3 kpc from the Sun. Comparison with observed numbers shows that the close binary produced WR stars should constitute a significant fraction of all WR stars, the exact fraction being dependent on the lower mass limit for WR star production (and also the duration of WR characteristics in the helium star's lifetime). The mass transfer processes in close binary systems probably allow this limit to be lower than in the case of a single WR star. Another favourable comparison regards the computed and observed numbers of persistent strong, massive X-ray binaries. Finally, second-phase WR stars are likely to comprise 5 — 10 % of the number of normal, first-stage WR binaries.