A reducing agent dosing valve (24) on an exhaust system (12) of an internal combustion engine (10), having a pump (32) which generates an injection pressure (p_24), and having a control unit (14) which actuates the reducing agent dosing valve (24) with actuation signals is presented, wherein the actuation signals are formed in a manner dependent on a reducing agent pressure (p_36) prevailing at the pump side. The method is distinguished by the fact that the actuation signals are formed additionally in a manner dependent on at least one estimated value for an influence of a drop in the injection pressure (p_24), which occurs upon the opening of the reducing agent dosing valve (24), on the injected reducing agent quantity.