DECORATED-BOX-DIAGRAM CONTRIBUTIONS TO BHABHA SCATTERING .1.

We evaluate, in the high-energy limit, s >> Absolute value of t >> m2 >> lambda2, the sum of amplitudes corresponding to a class of Feynman diagrams describing two-loop virtual photonic corrections to Bhabha sc attering. The diagrams considered are box and crossed-box diagrams wit h an extra photon decorating one of the fermion lines. The mathematica l method employed is that of Mellin transforms. In the eikonal approxi mation, this sum of two-loop amplitudes has previously been evaluated, and found to be equal to the sum of the box and crossed-box amplitude s, multiplied by the electric form factor of the electron. We obtain a similar factorization, but with the form factor replaced by another e xpression involving the logarithms log(lambda2/m2) and log(lambda2/Abs olute value of t).