Method for operating an exhaust gas purification system with an SCR catalytic converter to purify exhaust gas of a motor vehicle internal combustion engine, wherein an ammonia-containing reducing agent is metered to the exhaust gas by a metering unit that can be controlled by a control unit and exhaust gas enriched with ammonia corresponding to the metering operation is fed to the SCR catalytic converter, wherein a computational model calculates as follows: - an ammonia filling level value for a filling level of ammonia stored in the SCR catalytic converter and - a model metering rate for metering the reducing agent into the exhaust gas, with which a target filling level, predefined by the computational model, of ammonia stored in the SCR catalytic converter, and / or a target efficiency, predefined by the computational model, for a nitrogen oxide conversion (U NOx) with ammonia stored in the SCR catalytic converter and / or fed to the SCR catalytic converter are at least approximately achieved, wherein - a correction by a variable long-term adaptation factor to a target metering rate is provided for the model metering rate, - a correction by a variable short-term adaptation factor to an assumed target filling level is provided for the ammonia filling level value, and - the metering unit is controlled to discharge the target metering rate, characterised in that through integration in successive integration cycles of pre-settable length, a nitrogen oxide raw emission value (NOx in), a nitrogen oxide pure emission estimated value (NOx outcalc) and a nitrogen oxide pure emission measurement value (NOx outmes) and furthermore, as an adaptation characteristic value, a difference relating to the nitrogen oxide raw emission value (NOx in) with respect to the nitrogen oxide pure emission measurement value (NOx outmes) and the nitrogen oxide pure emission estimated value (NOx outcalc) are determined in parallel, wherein the adaptation characteristic value is used to assess the need for a long-term and / or short term adaptation. - an ammonia filling level value for a filling level of ammonia stored in the SCR catalytic converter and - a model metering rate for metering the reducing agent into the exhaust gas, with which a target filling level, predefined by the computational model, of ammonia stored in the SCR catalytic converter, and / or a target efficiency, predefined by the computational model, for a nitrogen oxide conversion (U NOx) with ammonia stored in the SCR catalytic converter and / or fed to the SCR catalytic converter are at least approximately achieved, wherein - a correction by a variable long-term adaptation factor to a target metering rate is provided for the model metering rate, - a correction by a variable short-term adaptation factor to an assumed target filling level is provided for the ammonia filling level value, and - the metering unit is controlled to discharge the target metering rate, characterised in that through integration in successive integration cycles of pre-settable length, a nitrogen oxide raw emission value (NOx in), a nitrogen oxide pure emission estimated value (NOx outcalc) and a nitrogen oxide pure emission measurement value (NOx outmes) and furthermore, as an adaptation characteristic value, a difference relating to the nitrogen oxide raw emission value (NOx in) with respect to the nitrogen oxide pure emission measurement value (NOx outmes) and the nitrogen oxide pure emission estimated value (NOx outcalc) are determined in parallel, wherein the adaptation characteristic value is used to assess the need for a long-term and / or short term adaptation.