  The computation of the correction \Delta r in the W-Z mass correlation,
derived from muon decay, is described at the two-loop level in the Standard
Model. Technical aspects which become relevant at this level are studied, e.g.
gauge-parameter independent mass renormalization, ghost-sector renormalization
and the treatment of \gamma_5. Exact results for \Delta r and the W mass
prediction including O(\alpha^2) corrections with fermion loops are presented
and compared with previous results of a next-to-leading order expansion in the
top-quark mass.
