A method for operating a dosing unit for dosing reducing agent into an exhaust gas treatment device for purifying the exhaust gases of an internal combustion engine, includes providing the dosing unit with at least one delivery pump, at least one injector and a line section for conducting reducing agent from the delivery pump to the injector. The dosing unit is first operated for dosing reducing agent into the exhaust gas treatment device. Then, the dosing unit is shut off. Subsequently, a first pressure is maintained in the line section for at least a first time period, with the first pressure exceeding atmospheric pressure. A motor vehicle having the dosing unit is also provided.