The tank venting device has a fuel vapor reservoir connected to a fuel tank to deliver escaping fuel vapors to the fuel vapor reservoir, and is connected to the internal combustion engine in such a manner that during a tank venting operation the fuel vapors contained in the fuel vapor reservoir are delivered as regeneration gas. To check the operability of the venting device the fuel concentration in the regeneration gas is ascertained at a minimum of two different points in time during the venting operation. The fuel concentration values in the regeneration gas are compared with respective reference values representing the regeneration gas fuel concentration in the situation in which no additional fuel vapors are delivered during the venting operation. The assessment of the venting device operability is carried out by comparison of the values ascertained for the fuel concentration in the regeneration gas with the reference values.