A method is provided for ascertaining a NOx concentration and an NH3 slip downstream from an SCR catalytic converter of an internal combustion engine of a vehicle. State variables of an internal combustion engine as first input variables and an updated NH3 fill level of the SCR catalytic converter as a second input variable cooperate with at least one machine learning algorithm or at least one stochastic model. The at least one machine learning algorithm or at least one stochastic model calculates the NOx concentration and the NH3 slip downstream from the SCR catalytic converter as a function of the first input variables and the second input variables and output the same as output variables.