  Experiments at the future colliders LHC and ILC will, for the first time,
explore electroweak reactions at energies in the TeV region, i.e. far beyond
the masses of the W and Z bosons. In exclusive processes without the emission
of massive gauge bosons double-logarithmic contributions, so-called Sudakov
logarithms, will then become relevant. Precise theoretical predictions require
the knowledge of the complete logarithmic two-loop corrections in the high
energy limit, thus exceeding the approximation through the leading powers of
logarithms known so far. This PhD thesis is focussed on the calculation of
analytic two-loop corrections to the form factor of an Abelian vector current.
It also studies with the help of evolution equations the consequences of these
results for electroweak cross sections of four-fermion processes. Contributions
from the Higgs boson and the mass difference between the W and the Z boson are
considered as well, and the factorization of the singular contributions from
the massless photon is demonstrated. The results represent theoretical two-loop
predictions for four-fermion processes in the accuracy needed for the precision
experiments at the ILC.
