NOVELTY - The gas stream is passed through compression stages (103,106) in series to form a compressed stream. At least a portion of the organic component is withdrawn from the compressed stream as a withdrawn stream, leaving a remaining stream. The remaining stream is subjected to membrane separation steps (111,114). At least a portion of the separated stream is recirculated to compression stage (106 or 103).    USE - For separation of organic component e.g. saturated hydrocarbon, unsaturated hydrocarbon and substituted hydrocarbons e.g. halogenated hydrocarbons, from gas stream. The method is useful for separation of off-gas stream from refineries to recover hydrogen and/or LPG, purification of natural gas to remove C3+ hydrocarbons, particularly for separation of C2+ hydrocarbons from nitrogen and for treating olefin/nitrogen off-gas stream from polyolefin manufacturing process.    ADVANTAGE - The separation method reduces load on the compression stage, thus allowing use of smaller compressor package. A lower total compressor horsepower is required to achieve the same degree of separation and recovery as achieved by circulating entire membrane permeate to front of compressor train. The recovery of gas is increased to 95% or more, without loss of gas purity. The method is suitable for separating off-gas stream from refineries to recover hydrogen and/or LPG, and purifying natural gas to remove C3+ hydrocarbons, particularly for separating C2+ hydrocarbons from nitrogen, and for treating olefin/nitrogen off-gas stream. The organic component is separated from gas stream by energy-and-cost efficient method. Any type of compressor is used for compression step, and the separation steps are performed using membranes selective in favor of organic component over gas.    DETAILED DESCRIPTION - The gas stream is passed through compression stages in series to form a compressed stream. Portion(s) of organic component is withdrawn from compressed stream as a withdrawn stream, leaving a remaining stream. The remaining stream is subjected to membrane separation steps. Portion(s) of the separated stream is recirculated to compression stage (106 or 103). The membrane separation step (111) is performed by providing a membrane (M1) having feed side (F1) and permeate side (P1), passing remaining stream over feed side (F1) under pressure drop conditions between feed side (F1) and permeate side (P1), withdrawing residue (R1) stream enriched in gas (G2) compared with the remaining stream from feed side (F1) and withdrawing permeate (P1) enriched in organic component compared with remaining stream from the permeate side. The membrane separation step (114) is performed by providing another membrane (M2) having feed side (F2) and permeate side (P2), passing residue (R1) over feed side (F2) under pressure drop conditions between feed side (F2) and permeate side (P2), withdrawing residue (R2) stream enriched in gas (G2) compared with residue (R1) stream and withdrawing permeate (P2) enriched in organic component compared with residue (R1) stream from permeate side (P2).    INDEPENDENT CLAIMS are included for:    (1) a process for treating an off-gas stream containing olefin from polyolefin manufacturing operation;    (2) a process for treating a refinery off-gas stream containing hydrogen and C3+ hydrocarbon; and    (3) a process for treating a natural gas stream containing methane and C3+ hydrocarbon.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic drawing of separation of organic component from gas stream.    Compression stages (103,106)    Membrane separation steps (111,114)