Hydrogen (H2) is commonly considered as one of the most promising carbon-free energy carriers allowing for a decarbonization of combustion applications, for instance by retrofitting of conventional diesel internal combustion engines (ICEs). Although modern H2-ICEs emit only comparably low levels of nitrogen oxides (NOx), efficient catalytic converters are mandatory for exhaust gas after-treatment in order to establish near-zero emission applications. In this context, the present study evaluates the performance of a commercial state-of-the-art oxidation catalyst (OC) and of a catalyst for selective catalytic reduction (SCR) that are typically used for emission reduction from diesel exhausts under conditions representative for H2-fueled ICEs, namely oxygen-rich exhausts with high water vapor levels, comparably low temperatures, and potentially considerable levels of unburnt H2. Herein, the OC is supposed to convert H2 slippage, which can occur due to incomplete combustion, and to oxidize NO to NO2, which enables an efficient NOx removal over the SCR catalyst. While the vanadia-based SCR catalyst was barely affected by high water vapor levels, the presence of H2, or hydrothermal aging, H2O inhibited NO to NO2 oxidation over the OC and hydrothermal aging with 20 vol.-% H2O resulted in significant deactivation of the OC. At the cost of producing the inhibitor H2O and the greenhouse gas N2O, the presence of H2 facilitates a fast light-off due to temperature generation. These results underscore the importance of developing suitable catalyst operation strategies that account for efficient pollutant conversion and avoid secondary emissions formation.