A vacuum pump for differentially pumping a plurality of chambers, the vacuum pump comprising: a housing which houses a plurality of compound pumping arrangements (28, 30) supported for independent rotation one from another on respective drive shafts by separate motors; a first housing inlet for receiving fluid from a first chamber; a second housing inlet for receiving fluid from a second chamber; a first of the compound pumping arrangements comprising a first pumping section comprising a turbo molecular pumping mechanism and a second pumping section downstream from the first pumping section, the sections being arranged such that fluid entering the compound pump from the first inlet passes through the first and second pumping sections and fluid entering the compound pump from the second inlet passes through, of said sections, only the second section; the vacuum pump further comprising: a third housing inlet for receiving fluid from a third chamber; a fourth housing inlet for receiving fluid from a fourth chamber; a second of the compound pumping arrangements comprising a third pumping section comprising a turbo molecular pumping mechanism (44, 46, 48, 50) and a fourth (52, 54, 56) section downstream from the first pumping section, the sections being arranged such that fluid entering the second compound pumping arrangement from the third inlet passes through the third and fourth pumping sections and fluid entering the second compound pump from the fourth inlet passes through, of said sections, only the fourth section. a housing which houses a plurality of compound pumping arrangements (28, 30) supported for independent rotation one from another on respective drive shafts by separate motors; a first housing inlet for receiving fluid from a first chamber; a second housing inlet for receiving fluid from a second chamber; a first of the compound pumping arrangements comprising a first pumping section comprising a turbo molecular pumping mechanism and a second pumping section downstream from the first pumping section, the sections being arranged such that fluid entering the compound pump from the first inlet passes through the first and second pumping sections and fluid entering the compound pump from the second inlet passes through, of said sections, only the second section; the vacuum pump further comprising: a third housing inlet for receiving fluid from a third chamber; a fourth housing inlet for receiving fluid from a fourth chamber; a second of the compound pumping arrangements comprising a third pumping section comprising a turbo molecular pumping mechanism (44, 46, 48, 50) and a fourth (52, 54, 56) section downstream from the first pumping section, the sections being arranged such that fluid entering the second compound pumping arrangement from the third inlet passes through the third and fourth pumping sections and fluid entering the second compound pump from the fourth inlet passes through, of said sections, only the fourth section. a third housing inlet for receiving fluid from a third chamber; a fourth housing inlet for receiving fluid from a fourth chamber; a second of the compound pumping arrangements comprising a third pumping section comprising a turbo molecular pumping mechanism (44, 46, 48, 50) and a fourth (52, 54, 56) section downstream from the first pumping section, the sections being arranged such that fluid entering the second compound pumping arrangement from the third inlet passes through the third and fourth pumping sections and fluid entering the second compound pump from the fourth inlet passes through, of said sections, only the fourth section.