  We discuss the renormalization of mixing angles for theories with extended
scalar sectors. Motivated by shortcomings of existing schemes for mixing
angles, we review existing renormalization schemes and introduce new ones based
on on-shell conditions or symmetry requirements such as rigid or
background-field gauge invariance. Considering in particular the
renormalization of the mixing angles in the Two-Higgs-Doublet Model and the
Higgs-Singlet Extension of the Standard Model, we compare electroweak
corrections within these models for a selection of renormalization schemes. As
specific examples, we present next-to-leading-order results on the four-fermion
decays of heavy and light CP-even Higgs bosons, $H_1/H_2\to WW/Z Z\to4f$, and
on electroweak Higgs-boson production processes, i.e. Higgs-strahlung and
vector-boson fusion. We find that our new proposals for on-shell and
symmetry-based renormalization conditions are well-behaved for the considered
benchmark scenarios in both models.
