O(GAMMA) CORRECTIONS TO W-PAIR PRODUCTION IN E- AND GAMMA-GAMMA-COLLISIONS(E)

Several schemes to introduce finite width effects to reactions involvi ng unstable elementary particles are given and the differences between them are investigated. The effects of the different schemes are inves tigated numerically for W pair production. In e+e- --> W+W- we find th at the effect of the non-resonant graphs cannot be neglected for squar e-root s greater-than-or-equal-to 400 GeV. There is no difference betw een the various schemes to add these to the resonant graphs away from threshold, although some violate gauge invariance. On the other hand, in the reaction gammagamma --> W+W- the effect of the non-resonant gra phs is large everywhere, due to the t-channel pole. However, even requ iring that the outgoing lepton is observable (p(perpendicular-to) > 0. 02 square-root s) reduces the contribution to about 1%. Again, the sch eme dependence is negligible here.