PURPOSE: To provide a process for producing an alkene polymer from a starting material containing a specified impurity.

CONSTITUTION: An ethylene stream containing ethane as an impurity or a propylene stream containing propane as an impurity is brought into contact with a polymerization catalyst to produce a polymer product containing unreacted ethylene or propylene and the corresponding alkane. A gaseous mixture containing ethylene or propylene and the corresponding alkane is separated from the polymer product and subjected to adsorption at a temperature of 50-200°C in a bed of an absorbent which selectively absorbs an alkene to thereby adsorptively separate substantially all of the propylene or ethylene from the gaseous mixture. The ethylene or propylene is desorbed from the adsorbent and is recirculated into the polymerization zone. The process is operated at a low conversion/pass by recirculating unreacted monomer. The adsorption unit may be provided on upstream or downstream of the polymrerizer.