A method for producing a gasoline boiling range product, which method comprises: extracting light olefins including ethylene and propylene from a mixed light olefin feed stream comprising ethylene and propylene by passing the mixed light olefin feed stream in countercurrent contact with a liquid first aromatic feed stream comprising single ring aromatic compounds including benzene at a temperature not greater than 120°C and a pressure up to 3,500 kPag to dissolve olefins in the liquid first aromatic feed stream, thereby forming a mixed olefin/aromatic stream and an unsorbed olefin effluent stream, passing the mixed olefin/aromatic stream containing dissolved, extracted olefins to a first alkylation step in which the single ring aromatic compounds are alkylated with the dissolved, extracted olefins over a fixed bed of a solid molecular sieve alkylation catalyst comprising a zeolite of the MWW family in a liquid phase reaction at a temperature in the range of 120 to 250° C, a pressure not more than 7,500 kPag, and an olefin:aromatics ratio of 0.5:1 to 2:1 to form a first gasoline boiling range product containing alkylaromatics, and, passing the unsorbed olefin effluent stream containing unsorbed olefins to a second alkylation step in which the mixed light olefin feed stream containing unsorbed olefins is used to alkylate aromatic compounds in a second aromatic feed stream in a fixed bed catalytic, vapor phase reaction carried out at a higher temperature than the temperature of the first alkylation step, and over a catalyst comprising an intermediate pore size zeolite which is more active for ethylene conversion than the MWW type zeolite used in the first alkylation step, to form a second gasoline boiling range product containing alkylaromatics. extracting light olefins including ethylene and propylene from a mixed light olefin feed stream comprising ethylene and propylene by passing the mixed light olefin feed stream in countercurrent contact with a liquid first aromatic feed stream comprising single ring aromatic compounds including benzene at a temperature not greater than 120°C and a pressure up to 3,500 kPag to dissolve olefins in the liquid first aromatic feed stream, thereby forming a mixed olefin/aromatic stream and an unsorbed olefin effluent stream, passing the mixed olefin/aromatic stream containing dissolved, extracted olefins to a first alkylation step in which the single ring aromatic compounds are alkylated with the dissolved, extracted olefins over a fixed bed of a solid molecular sieve alkylation catalyst comprising a zeolite of the MWW family in a liquid phase reaction at a temperature in the range of 120 to 250° C, a pressure not more than 7,500 kPag, and an olefin:aromatics ratio of 0.5:1 to 2:1 to form a first gasoline boiling range product containing alkylaromatics, and, passing the unsorbed olefin effluent stream containing unsorbed olefins to a second alkylation step in which the mixed light olefin feed stream containing unsorbed olefins is used to alkylate aromatic compounds in a second aromatic feed stream in a fixed bed catalytic, vapor phase reaction carried out at a higher temperature than the temperature of the first alkylation step, and over a catalyst comprising an intermediate pore size zeolite which is more active for ethylene conversion than the MWW type zeolite used in the first alkylation step, to form a second gasoline boiling range product containing alkylaromatics.