A positive displacement dry pump comprising: a plurality of vacuum pumping stages (12, 14, 16, 18) comprising a respective plurality of pumping mechanisms (20, 22, 24, 25) driven by one or more drive shafts (28, 30) for pumping fluid in series through the pumping stages from a pump inlet at the high vacuum stage to a pump outlet at the low vacuum stage; a lubrication chamber housing a bearing assembly (50,52) for supporting the drive shaft for rotational movement, the drive shaft extending from the high vacuum stage to the lubrication chamber through an opening of a head plate of the lubrication chamber; an inter-stage purge port (62, 86) through which purge gas can enter the pump at an inter-stage location downstream of the high vacuum stage and pass only through the or each vacuum pumping stage downstream of the inter-stage purge port; a lubrication chamber purge port located in the lubrication chamber through which purge gas can flow from a source of purge gas; wherein the inter-stage purge port (62, 86) is connected to the lubrication chamber by one or more conduits (70,72) configured so that the purge gas pressure in the lubrication chamber is variable in response to changes in pressure within the vacuum pump at the inter-stage purge port and the pressure within the vacuum pump at the inter-stage purge port is responsive to changes in fluid pressure in the high vacuum stage so that a variation in fluid pressure in the high vacuum stage causes a variation in the purge gas pressure in the lubrication chamber thereby resisting the passage of pumped fluid from the high vacuum chamber to the lubrication chamber through the opening of the head plate during use. a plurality of vacuum pumping stages (12, 14, 16, 18) comprising a respective plurality of pumping mechanisms (20, 22, 24, 25) driven by one or more drive shafts (28, 30) for pumping fluid in series through the pumping stages from a pump inlet at the high vacuum stage to a pump outlet at the low vacuum stage; a lubrication chamber housing a bearing assembly (50,52) for supporting the drive shaft for rotational movement, the drive shaft extending from the high vacuum stage to the lubrication chamber through an opening of a head plate of the lubrication chamber; an inter-stage purge port (62, 86) through which purge gas can enter the pump at an inter-stage location downstream of the high vacuum stage and pass only through the or each vacuum pumping stage downstream of the inter-stage purge port; a lubrication chamber purge port located in the lubrication chamber through which purge gas can flow from a source of purge gas; wherein the inter-stage purge port (62, 86) is connected to the lubrication chamber by one or more conduits (70,72) configured so that the purge gas pressure in the lubrication chamber is variable in response to changes in pressure within the vacuum pump at the inter-stage purge port and the pressure within the vacuum pump at the inter-stage purge port is responsive to changes in fluid pressure in the high vacuum stage so that a variation in fluid pressure in the high vacuum stage causes a variation in the purge gas pressure in the lubrication chamber thereby resisting the passage of pumped fluid from the high vacuum chamber to the lubrication chamber through the opening of the head plate during use.