Simple equilibrium theory-based formulations were derived and used to investigate the feasibility of complete cleanup in and compare the performances of pressure swing adsorption (PSA) and vacuum swing adsorption (VSA) air purification processes. Three representative contaminants were investigated (dimethyl methylphosphonate, benzene, and butane), all on activated carbon. For these systems, complete cleanup during every cycle was always possible in a VSA process; and it was also possible in a PSA process, but only for the two less strongly adsorbed systems and only when their feed mole fractions were less than some specific value. Otherwise, a subatmospheric purge pressure was required by PSA no matter how high the feed pressure. The pressure ratio required for complete cleanup by PSA was generally several times higher than that required by VSA for the same feed mole fraction, except for the two less strongly adsorbed systems at very low feed mole fractions. For VSA and PSA processes with incomplete cleanup, VSA processed more feed than PSA; this advantage became more pronounced with stronger adsorbates and higher feed concentrations. The superiority of VSA over PSA also became more pronounced with higher pressure ratios and lower purge-to-feed ratios.