An integrated selective two-stage hydrocracking process for producing diesel and/or naphtha product streams, respectively boiling in the range from 180 °C to 370 °C and 36 °C to 180 °C, from a feedstock, including: a. separating the hydrocarbon feed into an aromatic-lean fraction and an aromatic-rich fraction by contacting the hydrocarbon feed and an effective quantity of extraction solvent in an extraction zone to produce an extract containing a major proportion of the aromatic content of the hydrocarbon feed and a portion of the extraction solvent and a raffinate containing a major proportion of the non-aromatic content of the hydrocarbon feed and a portion of the extraction solvent, separating at least a substantial portion of the extraction solvent from the raffinate and recovering the aromatic-lean fraction, and separating at least a substantial portion of the extraction solvent from the extract and recovering the aromatic-rich fraction, wherein the extraction solvent is selected from the group consisting of furfural, N-methyl-2-pyrrolidone, dimethylformamide, dimethylsulfoxide, phenol, nitrobenzene, sulfolanes, acetonitrile, and glycols; b. hydroprocessing the aromatic-rich fraction in a first vessel of a first stage hydroprocessing reaction zone operating under conditions effective to hydrotreat and hydrocrack at least a portion of aromatic compounds contained in the aromatic-rich fraction to produce a first vessel first stage hydroprocessing reaction zone effluent; c. hydroprocessing the aromatic-lean fraction in a second vessel of the first stage hydroprocessing reaction zone operating under conditions effective to hydrotreat and hydrocrack at least a portion of aromatic compounds contained in the aromatic-lean fraction to produce a second vessel first stage hydroprocessing reaction zone effluent; d. fractionating a mixture of first vessel first stage hydroprocessing reaction zone effluent and second vessel first stage hydroprocessing reaction zone effluent to produce one or more fractionating zone diesel and/or naphtha product streams and one or more fractionating zone bottoms streams; e. hydroprocessing at least a portion of the fractionating zone bottoms stream in a second stage hydroprocessing reaction zone to produce a second stage hydroprocessing reaction zone effluent; and f. conveying the second stage hydroprocessing reaction zone effluent to the step of fractionating. a. separating the hydrocarbon feed into an aromatic-lean fraction and an aromatic-rich fraction by contacting the hydrocarbon feed and an effective quantity of extraction solvent in an extraction zone to produce an extract containing a major proportion of the aromatic content of the hydrocarbon feed and a portion of the extraction solvent and a raffinate containing a major proportion of the non-aromatic content of the hydrocarbon feed and a portion of the extraction solvent, separating at least a substantial portion of the extraction solvent from the raffinate and recovering the aromatic-lean fraction, and separating at least a substantial portion of the extraction solvent from the extract and recovering the aromatic-rich fraction, wherein the extraction solvent is selected from the group consisting of furfural, N-methyl-2-pyrrolidone, dimethylformamide, dimethylsulfoxide, phenol, nitrobenzene, sulfolanes, acetonitrile, and glycols; b. hydroprocessing the aromatic-rich fraction in a first vessel of a first stage hydroprocessing reaction zone operating under conditions effective to hydrotreat and hydrocrack at least a portion of aromatic compounds contained in the aromatic-rich fraction to produce a first vessel first stage hydroprocessing reaction zone effluent; c. hydroprocessing the aromatic-lean fraction in a second vessel of the first stage hydroprocessing reaction zone operating under conditions effective to hydrotreat and hydrocrack at least a portion of aromatic compounds contained in the aromatic-lean fraction to produce a second vessel first stage hydroprocessing reaction zone effluent; d. fractionating a mixture of first vessel first stage hydroprocessing reaction zone effluent and second vessel first stage hydroprocessing reaction zone effluent to produce one or more fractionating zone diesel and/or naphtha product streams and one or more fractionating zone bottoms streams; e. hydroprocessing at least a portion of the fractionating zone bottoms stream in a second stage hydroprocessing reaction zone to produce a second stage hydroprocessing reaction zone effluent; and f. conveying the second stage hydroprocessing reaction zone effluent to the step of fractionating.