Recently two-loop electroweak corrections to the neutral current
four-fermion processes at high energies have been presented.
The basic ingredient of this calculation is the evaluation of the
two-loop corrections to the Abelian vector form factor in a
spontaneously broken SU(2) gauge model.
Whereas the final result and the derivation of the four-fermion
cross sections from evolution equations have been published earlier,
the calculation of the form factor from the two-loop Feynman
diagrams is presented for the first time in this paper.
We describe in detail the individual contributions to the form factor
and their calculation with the help of the expansion by regions
method and Mellin-Barnes representations.
