A method for operating an exhaust system, where the exhaust system has a first selective catalytic reduction (SCR) catalytic converter close to the engine and a second SCR catalytic converter arranged downstream of the first. A respective quantity of reducing agent to be introduced into the exhaust gas by a respective dosing element is set depending on a first temperature of the first SCR catalytic converter, where during a period of time during which the first temperature exceeds a predeterminable first threshold value and a second temperature of the second SCR catalytic converter exceeds a predeterminable second threshold value, which is lower than the first threshold value, the introduction of the reducing agent into the exhaust gas with regard to the dosing elements takes place exclusively via the second dosing element such that during the period of time, no introduction of the reducing agent into the exhaust gas takes place.