A tank-venting arrangement includes: a tank having a tank closure; an electrically drivable check valve; an adsorption filter; connecting lines for interconnecting the above components; a difference pressure sensor which measures the pressure difference between the pressure in the tank and the ambient pressure and supplies a pressure difference signal; a comparator which, at least for a running engine, compares the pressure difference signal to upper and lower threshold values and supplies an opening signal to the check valve to open the latter when the pressure difference signal is greater than the upper threshold value and a closure signal for closing the check valve when the pressure difference signal drops below the lower threshold value; and, a detector unit which supplies an opening signal to the check valve for opening the check valve when the sensor determines a possible opening of the tank and a closure signal for closing the check valve when the sensor determines a possible closure of the tank. With the aid of the check valve and the difference pressure sensor which measures the pressure difference between the pressure in the tank and the ambient pressure, the tank-venting arrangement can be so operated that at least for a running engine, a desired maximum overpressure in the tank can be obtained relative to the ambient pressure independently of the extent of the underpressure in that part of the arrangement forward of the check valve.