In a process for the production of a polyolefin, an olefin monomer is polymerised said polyolefin and residual monomer is recovered. A gas stream comprising the monomer and nitrogen is subjected to a PSA process in which said monomer is adsorbed on a periodically regenerated silica gel or alumina adsorbent to recover a purified gas stream containing said olefin and a nitrogen rich stream containing no less than 99% nitrogen and containing no less than 50% of the nitrogen content of the gas feed to the PSA process.