A dry-running vane gas pump includes a pump housing which forms a pump chamber, a pump rotor with at least one displaceable slide element which pump rotor is rotatably supported in the pump chamber, at least one fluid inlet opening associated with the pump chamber, a first fluid outlet opening associated with the pump chamber, a second fluid outlet opening associated with the pump chamber, and a non-return valve which closes the first fluid outlet opening. The second fluid outlet opening is permanently open. The first fluid outlet opening is arranged before the second fluid outlet opening in a direction of rotation of the pump rotor.