A method and a device are provided for operating an electrically driven motor vehicle with a battery-fed electric drive motor and a generator-coupled internal combustion engine for providing electric energy for the battery. An internal combustion engine is operated based on the state of charge of the battery. In the method, a route to a previously entered destination is determined by way of a navigation system, and it is checked periodically, based on the particular route, a detected charge level of the battery and a detected energy consumption, whether the destination will be reached or whether there is a range gap to the destination. When a range gap is determined, it is determined, whether the destination can be reached in at least one specified energy saving operating mode, in which the energy consumption is reduced, or whether the destination will be reached only in REX operating mode. The driver is sent a corresponding recommendation. If no decision is made by the driver, then the REX operating mode is activated as soon as it is determined that this mode is necessary to bridge the range gap.