  Recently exact results for the complete fermionic two-loop contributions to
the prediction for the W-boson mass from muon decay in the electroweak Standard
Model have been published [hep-ph/0007091]. This paper illustrates the
techniques that have been applied for this calculation, in particular the
renormalisation procedure and the treatment of IR-divergent QED contributions.
Numerical results are presented in terms of simple parametrisation formulae and
compared in detail with a previous result of an expansion up to next-to-leading
order in the top-quark mass. An estimate of the remaining theoretical
uncertainties of the MW-prediction from unknown higher-order corrections is
given. For the bosonic two-loop corrections a partial result is presented,
yielding the Higgs-mass dependence of these contributions.
