A hydrocracking process is provided for treating a first heavy hydrocarbon feedstream and a second heavy hydrocarbon feedstream, in which the first heavy hydrocarbon feedstream contains undesired nitrogen-containing compounds, sulfur-containing compounds and poly-nuclear aromatic compounds. The first heavy hydrocarbon feedstream is contacted with adsorbent material to produce a treated heavy hydrocarbon stream. The second heavy hydrocarbon feedstream is combined with the treated heavy hydrocarbon stream, and this combined stream is charged to a hydrocracking reaction unit. The hydrocracked effluent is fractioned to recover hydrocracked products and a bottoms stream containing heavy poly-nuclear aromatic compounds. Fractionator bottoms are also contacted with adsorbent material to produce an adsorbent-treated fractionator bottoms stream having a reduced content of heavy poly-nuclear aromatic compounds, and are recycled to the hydrocracking reaction unit.