  We study the NNLO radiative corrections of enhanced electroweak strength to
the lineshape of the Higgs boson in the processes ($\mu^+\mu^- \to H \to ZZ$)
and ($\mu^+\mu^- \to H \to t\bar t$), which are of interest for Higgs searches
at a possible muon collider. We give the radiative corrections both in the
on-shell renormalization scheme and in the pole renormalization scheme. The
pole scheme appears to have better convergence properties, in agreement with
previous results regarding the position of the Higgs pole in the complex plane.
