  The Higgs-mass dependence of the two-loop contributions to muon decay is
analyzed at the two-loop level. Exact results are given for the Higgs-dependent
two-loop corrections associated with the fermions, i.e. no expansion in the
top-quark and the Higgs-boson mass is made. The remaining theoretical
uncertainties in the Higgs-mass dependence of $\Delta r$ are discussed.
