Process for hydrorefining biological feedstocks comprising: a) introducing a pretreated biological feedstock and a stream of hydrogen into a hydrorefining zone that uses at least one solid catalyst to catalyse hydrotreating reactions and to produce a liquid hydrorefining outflow; b) introducing said liquid hydrorefining outflow and a light-hydrocarbons-stripping fluid into a light-ends recovery zone, wherein said light-hydrocarbons-stripping fluid is contacted with said liquid hydrorefining outflow to create a recovered light ends stream and a gas-stripped liquid outflow stream; and c) introducing a feed stream combining said recovered light ends stream and a stream of the same light-hydrocarbons-stripping fluid as in step a) into a hydrogen production zone, said hydrogen production zone using the hydrocarbons present in said recovered light ends stream as feedstock to create at least a portion of said hydrogen stream used in step (a), or to create a hydrogen-rich vapour outflow stream, the process further comprising the following steps d) and e): d) introducing said gas-stripped liquid outflow stream into a secondary hydrorefining zone that uses at least one secondary solid catalyst to catalyse additional hydrorefining reactions to produce a secondary liquid hydrorefining outflow; e) introducing said hydrogen-rich vapour outflow stream into said secondary hydrorefining zone; then cascading excess hydrogen from said secondary hydrorefining zone into said hydrorefining zone. a) introducing a pretreated biological feedstock and a stream of hydrogen into a hydrorefining zone that uses at least one solid catalyst to catalyse hydrotreating reactions and to produce a liquid hydrorefining outflow; b) introducing said liquid hydrorefining outflow and a light-hydrocarbons-stripping fluid into a light-ends recovery zone, wherein said light-hydrocarbons-stripping fluid is contacted with said liquid hydrorefining outflow to create a recovered light ends stream and a gas-stripped liquid outflow stream; and c) introducing a feed stream combining said recovered light ends stream and a stream of the same light-hydrocarbons-stripping fluid as in step a) into a hydrogen production zone, said hydrogen production zone using the hydrocarbons present in said recovered light ends stream as feedstock to create at least a portion of said hydrogen stream used in step (a), or to create a hydrogen-rich vapour outflow stream, the process further comprising the following steps d) and e): d) introducing said gas-stripped liquid outflow stream into a secondary hydrorefining zone that uses at least one secondary solid catalyst to catalyse additional hydrorefining reactions to produce a secondary liquid hydrorefining outflow; e) introducing said hydrogen-rich vapour outflow stream into said secondary hydrorefining zone; then cascading excess hydrogen from said secondary hydrorefining zone into said hydrorefining zone. d) introducing said gas-stripped liquid outflow stream into a secondary hydrorefining zone that uses at least one secondary solid catalyst to catalyse additional hydrorefining reactions to produce a secondary liquid hydrorefining outflow; e) introducing said hydrogen-rich vapour outflow stream into said secondary hydrorefining zone; then cascading excess hydrogen from said secondary hydrorefining zone into said hydrorefining zone.