  The 2-Higgs-Doublet Model (2HDM) belongs to the simplest extensions of the
Standard Model (SM) Higgs sector that are in accordance with theoretical and
experimental constraints. In order to be able to properly investigate the
experimental Higgs data and, in the long term to distinguish between possible
models beyond the SM, precise predictions for the Higgs boson observables have
to be made available on the theory side. This requires the inclusion of the
higher order corrections. In this work, we investigate in detail the
renormalization of the 2HDM, a pre-requisite for the computation of higher
order corrections. We pay particular attention to the renormalization of the
mixing angles $\alpha$ and $\beta$, which diagonalize the Higgs mass matrices
and which enter all Higgs observables. The implications of various
renormalization schemes in next-to-leading order corrections to the sample
processes $H^\pm \to W^\pm h/H$ and $H \to ZZ$ are investigated. Based on our
findings, we will present a renormalization scheme that is at the same time
process independent, gauge independent and numerically stable.
