A method of processing a cracked gas feed stream containing hydrogen, methane, ethylene, propylene and other C 2, C 3, C 4, C 5, C 6 and heavier unsaturated hydrocarbons to separate said ethylene and propylene from at least some of said other unsaturated hydrocarbons and to hydrogenate at least some of said other unsaturated hydrocarbons without hydrogenating ethylene and propylene, the method comprising the steps of: a. introducing said feed stream into a first column comprising a catalytic distillation hydrogenation column containing at least one catalyst bed and containing fractionation zones and operating at a first pressure and concurrently: (i) selectively hydrogenating at least a portion of said other unsaturated hydrocarbons without hydrogenating said ethylene and propylene; (ii) separating by fractional distillation the resulting hydrocarbon mixture into a first column gross overhead stream containing unreacted hydrogen, methane, ethylene, propylene and C 4 and C 5 compounds and a first bottoms stream containing primarily C 6 and heavier hydrocarbons and some C 5, C 4, C 3 and C 2 unsaturated hydrocarbons; and (iii) operating said first column so as to maintain said first bottoms stream at a temperature less than 200°C; b. separating said first column gross overhead stream into a first column net overhead stream and a first column reflux stream and introducing said first column reflux stream back into said first column; c. introducing said first bottoms stream from said first column into a second column comprising a fractionation column operating at a second pressure lower than said first pressure and separating said first bottoms stream into a net bottoms stream containing C 6 and heavier hydrocarbons and a selected amount of C 5 hydrocarbons and into a second column gross overhead stream containing primarily additional C 6 and heavier hydrocarbons, and C 5, C 4, C 3 and C 2 hydrocarbons and operating said second column so as to maintain said net bottoms stream at a temperature less than 200°C; d. totally condensing and separating said second column gross overhead stream into a second column net overhead stream and a second column reflux stream and introducing said second column reflux stream back into said second column; and e. recycling said second column net overhead stream to said first column. a. introducing said feed stream into a first column comprising a catalytic distillation hydrogenation column containing at least one catalyst bed and containing fractionation zones and operating at a first pressure and concurrently: (i) selectively hydrogenating at least a portion of said other unsaturated hydrocarbons without hydrogenating said ethylene and propylene; (ii) separating by fractional distillation the resulting hydrocarbon mixture into a first column gross overhead stream containing unreacted hydrogen, methane, ethylene, propylene and C 4 and C 5 compounds and a first bottoms stream containing primarily C 6 and heavier hydrocarbons and some C 5, C 4, C 3 and C 2 unsaturated hydrocarbons; and (iii) operating said first column so as to maintain said first bottoms stream at a temperature less than 200°C; (i) selectively hydrogenating at least a portion of said other unsaturated hydrocarbons without hydrogenating said ethylene and propylene; (ii) separating by fractional distillation the resulting hydrocarbon mixture into a first column gross overhead stream containing unreacted hydrogen, methane, ethylene, propylene and C 4 and C 5 compounds and a first bottoms stream containing primarily C 6 and heavier hydrocarbons and some C 5, C 4, C 3 and C 2 unsaturated hydrocarbons; and (iii) operating said first column so as to maintain said first bottoms stream at a temperature less than 200°C; b. separating said first column gross overhead stream into a first column net overhead stream and a first column reflux stream and introducing said first column reflux stream back into said first column; c. introducing said first bottoms stream from said first column into a second column comprising a fractionation column operating at a second pressure lower than said first pressure and separating said first bottoms stream into a net bottoms stream containing C 6 and heavier hydrocarbons and a selected amount of C 5 hydrocarbons and into a second column gross overhead stream containing primarily additional C 6 and heavier hydrocarbons, and C 5, C 4, C 3 and C 2 hydrocarbons and operating said second column so as to maintain said net bottoms stream at a temperature less than 200°C; d. totally condensing and separating said second column gross overhead stream into a second column net overhead stream and a second column reflux stream and introducing said second column reflux stream back into said second column; and e. recycling said second column net overhead stream to said first column.