A process for hydrocracking a hydrocarbon feed, comprising: a) contacting a hydrocarbon feed in a hydrocracking zone with a hydrogen-containing gas and a catalytically effective amount of a hydrocracking catalyst under hydrocracking conditions thereby resulting in a lower boiling hydrocarbon liquid phase and a vapor phase containing hydrogen and light hydrocarbons; b) separating the lower boiling hydrocarbon liquid phase and the vapor phase; c) removing at least a portion of the light hydrocarbons from at least a portion of the vapor phase, thereby increasing its hydrogen concentration, in a rapid cycle pressure swing adsorption unit containing a plurality of adsorbent beds and having a total cycle time, t TOT, of less than 30 seconds and a pressure drop within each adsorbent bed of greater than 1.2 kPa (5 inches of water) per 0.3 m (1 foot) of bed length, wherein the light hydrocarbons are removed as a tail gas from the rapid cycle pressure swing adsorption unit at a pressure greater than or equal to 0.41 MPa (60 psig); and d) recycling at least a portion of the vapor phase of step c) above having an increased concentration of hydrogen to the hydrocracking zone; wherein the total cycle time, t TOT, to separate the hydrogen containing stream into a product gas and a tail gas is given by the formula: t TOT = t F + t CO + t CN + t P + t RP where t F = a time period for conducting the vapor phase into the rapid cycle pressure swing adsorption unit which adsorbs the gaseous compounds other than hydrogen, and passing hydrogen out of the rapid cycle pressure swing adsorption unit; t CO = a co-current depressurization time; t CN = a counter-current depressurization time; t P = a purge time; and t RP = a repressurization time; and wherein when the hydrogen product purity to feed purity ratio, P%/F%, is greater than 1.1, the rate of hydrogen recovery, R%, is greater than 80%; and when the hydrogen product purity to feed purity ratio, P%/F%, is less than 1.1, the rate of hydrogen recovery, R%, is greater than 90%, wherein P% is the purity of the product gas in mol%, F% is the mole percentage of the feed gas which is hydrogen, and R% is the ratio of the amount of hydrogen retained in the product to the amount of hydrogen available in the feed. a) contacting a hydrocarbon feed in a hydrocracking zone with a hydrogen-containing gas and a catalytically effective amount of a hydrocracking catalyst under hydrocracking conditions thereby resulting in a lower boiling hydrocarbon liquid phase and a vapor phase containing hydrogen and light hydrocarbons; b) separating the lower boiling hydrocarbon liquid phase and the vapor phase; c) removing at least a portion of the light hydrocarbons from at least a portion of the vapor phase, thereby increasing its hydrogen concentration, in a rapid cycle pressure swing adsorption unit containing a plurality of adsorbent beds and having a total cycle time, t TOT, of less than 30 seconds and a pressure drop within each adsorbent bed of greater than 1.2 kPa (5 inches of water) per 0.3 m (1 foot) of bed length, wherein the light hydrocarbons are removed as a tail gas from the rapid cycle pressure swing adsorption unit at a pressure greater than or equal to 0.41 MPa (60 psig); and d) recycling at least a portion of the vapor phase of step c) above having an increased concentration of hydrogen to the hydrocracking zone; t F = a time period for conducting the vapor phase into the rapid cycle pressure swing adsorption unit which adsorbs the gaseous compounds other than hydrogen, and passing hydrogen out of the rapid cycle pressure swing adsorption unit; t CO = a co-current depressurization time; t CN = a counter-current depressurization time; t P = a purge time; and t RP = a repressurization time;