polyolefins are produced by a process which includes the steps of : polymerizing an olefin in a reaction zone ; removing unreacted olefin from the polymer in a flash chamber and recycling the unreacted olefin to the reaction zone ; stripping unreacted olefin from the polymer by passing a stripping gas through the polymer in a stripping zone ; passing the unreacted olefin from the stripping zone at superatmospheric pressure through an adsorbent which selectively adsorbs olefins ; depressurizing the adsorbent to produce a substantially pure olefin and recycling the substantially pure olefin to the reaction zone ; purging the adsorbent bed with a nonadsorbable gas to remove residual unreacted olefin from the adsorbent ; and passing the purge gas - unreacted olefin to the stripping zone to be used as stripping gas .