In a process for producing an olefin polymer, an olefin monomer is polymerized to produce a particulate polymer product containing unreacted monomer. The polymer product is contacted with an inert gas to strip hydrocarbon impurities therefrom and produce a stripped polymer product and a gaseous first effluent stream containing inert gas and hydrocarbons. The stripped polymer product is recovered and the first effluent stream is compressed and cooled to condense hydrocarbons contained therein and produce a gaseous second effluent stream. Part of the second effluent stream is contacted with a first membrane separator to produce a first hydrocarbon-enriched permeate stream and a first hydrocarbon-depleted residue stream. The first residue stream is contacted with a second membrane separator to produce a second hydrocarbon-enriched permeate stream and a second hydrocarbon-depleted residue stream. The second permeate stream and an oxidizing agent are supplied to a flameless thermal oxidation unit.