A physico-chemical model of a Cu-zeolite SCR/DPF-system involving NH₃ storage and SCR reactions as well as soot oxidation reactions with NO₂ has been developed and validated based on fundamental experimental investigations on synthetic gas test bench. The goal of the work was the quantitative modeling of NOx and NH₃ tailpipe emissions in transient test cycles in order to use the model for concept design analysis and the development of control strategies. Another focus was put on the impact of soot on SCR/DPF systems. In temperature-programmed desorption experiments, soot-loaded SCR/DPF filters showed a higher NH₃ storage capacity compared to soot-free samples. The measured effect was small, but could affect the NH₃ slip in vehicle applications. A bimodal desorption characteristic was measured for different adsorption temperatures and heating rates. Therefore, a multiple-site NH₃ adsorption and desorption model was implemented which proved to be in good agreement with the experimental findings. In steady-state NOx conversion experiments for NO₂/NOx ratios up to 50%, the SCR reactivity was unaffected by the soot loading under the applied test conditions reaching full conversion for a large temperature range. For even higher NO₂/NOx ratios, an increase in NOx conversion efficiency was detected for temperatures up to 250°C for soot-loaded filters. An extended SCR reaction mechanism involving reactions on two active sites, NH₄NO₃ formation and the inhibition by surface nitrate species was calibrated. The model was validated with NEDC data showing high model quality for both, NOx and NH₃ slip prediction. The same parameter set, derived from synthetic gas experiments, was used and an additional water adsorption model was calibrated. The transferability of the kinetics to real exhaust conditions was confirmed by supplementary simulations of FTP75 and US06 data. The promoting soot effect on NOx conversion was further investigated by modeling, resolving the local reaction of NO₂ in the soot layer and the change in the SCR stoichiometry.