A multi-stage reciprocating vacuum pump includes first (2) and second (4) pump chambers located in the pump housing (1) and in which respective pistons (6, 8) reciprocate, first and second conduits (14, 20) for communicating, respectively outlet and suction (15, 16) sides of the first pump chamber (2) with the suction side (17) of the second pump chamber (4), and shut-off elements (18, 21; 25) associated with the first and second conduits (14, 20) for selectively communicating the first and second conduits (14, 20) with the suction side (17) of the second pump chamber (4); and the method of operating the pump includes manipulating the shut-off elements so that the first and second conduits (14, 20) are selectively connected to the suction side (17) of the second pump chamber (4).