A Roots-type machine is connected to an enclosure to be evacuated via a suction inlet portion, and to a primary pump via a delivery outlet portion. A bellows is disposed transversely in the inlet portion, one end of the bellows being fixed in gastight manner in the wall, and the other end being closed and movable, so that the bellows forms a regulating member for regulating the gas-flow sectional area in the inlet portion. The outside face of the movable end of the bellows is subjected to the pressure in the inlet portion, and the inside face of the movable end is subjected to the pressure in the delivery outlet portion via a rod passing through the wall, and via a channel. The invention applies to Roots-type machines, in particular for automatically regulating the pumping speed so as to match it to the flow-rate of the corresponding primary pump.