Calculation of two-loop top-quark and Higgs-boson corrections in the electroweak Standard Model

A combination of algebraical and numerical techniques for calculating two-loop top-quark and Higgs-boson corrections to electroweak precision observables like $\Delta r$ or the $\rho$-parameter is presented. The renormalization is performed within the on-shell scheme. The results of the calculations are valid for arbitrary values of $m_t$, $M_H$ and of the gauge-boson masses. An example is treated where the full result is compared to the result obtained via an expansion up to next-to-leading order in $m_t$. As an application, results for the Higgs-mass dependent top-contributions to $\Delta r$ are given.