  Power-suppressed corrections arising from end-point integration regions to
the space-like vertex function of the massive eta'-meson virtual gluon
transition eta' - g*g* are computed. Calculations are performed within the
standard hard-scattering approach (HSA) and the running coupling method
supplemented by the infrared renormalon calculus. Contributions to the vertex
function from the quark and gluon contents of the eta' -meson are taken into
account and the Borel resummed expressions for F_{eta' g*g*}(Q2,\omega ,\eta),
as well as for F_{eta' g g*}}(Q^{2},\omega =\pm 1,\eta) and F_{eta'
g*g*}(Q^{2},\omega =0,\eta) are obtained. It is demonstrated that the
power-suppressed corrections \sim (\Lambda ^{2}/Q^{2})^{n}, in the explored
range of the total gluon virtuality 1 <Q2 < 25 GeV2, considerably enhance the
vertex function relative to the results found in the framework of the standard
HSA with a fixed coupling. Modifications generated by the eta ' -meson mass
effects are discussed.
