Calculation of fermionic two-loop contributions to muon decay

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.