A vacuum pump assembly which is driven by pulsating exhaust gases emanating from an internal combustion engine is disclosed. The pump assembly includes a double-acting pump means for pumping air from a vacuum source and having a reciprocable pumping member, an actuating means including a reciprocable actuating member drivingly connected to the pumping member and which is driven through first and second strokes to move the pumping member through first and second strokes, respectively, one side of the actuating member being in communication with the exhaust gases and with the actuating and pumping members being movable through their first strokes during the pressure increasing phase of each pressure pulsation and being moved through their second strokes by a nonlinear variable rate air spring means during each pressure decreasing phase of each pressure pulsation. The air spring means is in communication with the atmosphere via bleed hole means and with the latter being uncovered during low engine speeds and loads, being covered and uncovered by the reciprocating actuating member during intermediate engine speeds and loads and being covered during high engine speeds and loads whereby the pump assembly is operable to pump air from the vacuum source throughout a wide range of engine speeds and loads including high speeds and loads.