Methane was oxidatively coupled to ethylene with very high yield in a novel gas recycle reactor-separator operated in a batch or continuous flow mode. The recycled gas passes continuously through a molecular sieve trap in the recycle loop which adsorbs and thus protects from further oxidation a controllable percentage of ethylene and ethane. The products are obtained by subsequent heating of the molecular sieve trap. Ethylene yield up to 85%, i.e. 88% selectivity to ethylene at 97% CH4 conversion, has been obtained in the batch mode of operation using a Ag-Sm2O3 or Ag electrocatalyst and electrochemical supply of oxygen through a ZrO2-Y2O3 solid electrolyte. Using the continuous flow mode of operation with gaseous O-2 supply in the recycle loop and a Sr(1wt%)/La2O3 catalyst we have obtained ethylene yields up to 50%, i.e. 65% C2H4 selectivity at 76% CH4 conversion. The synergy of the catalytic and molecular sieve materials is discussed and modelled in view of the predominantly consecutive nature of the oxidative coupling of methane (OCM) network.