Based on the existing exact O(alpha) corrections to the differential c
ross-section for on-shell W-pair production derive a high-energy appro
ximation valid for energies much higher than all particle masses. In t
he angular range -0.9 < cos theta < 0.9 this approximation reproduces
the full virtual and soft-photonic O(alpha) result essentially to bett
er than 1% for energies above 1 TeV and better than 0.1% above 10 TeV.
Taking only the dominant terms of this high-energy approximation into
account the resulting approximation deviates from the full result by
about 3%. Finally an interpretation in terms of running couplings is g
iven for the fermionic contribution to the approximation.