Some of the most interesting Higgs-production processes at future e⁺e^- colliders are of the type e⁺e^-\to f\bar fH. We present a calculation of the complete O(\alpha ) corrections to these processes in the Standard Model for final-state neutrinos and top quarks. Initial-state radiation beyond  O(\alpha ) at the leading-logarithmic level as well as QCD corrections are also included. The electroweak corrections turn out to be sizable and reach the order of \pm 10% and will thus be an important part of precise theoretical predictions for future e⁺e^- colliders. Furthermore, an overview is given of a technique for a fast and reliable numerical calculation of multi-leg one-loop integrals. The method is numerically stable also for exceptional momentum configurations and easily allows the introduction of complex masses and the calculation of higher orders in the expansion around D=4.

PACS numbers: 12.15.Lk