A multi-stage catalytic hydrogenation and hydroconversion process for heavy hydrocarbon feed materials such as coal, heavy petroleum fractions, and plastic waste materials. In the process, the feedstock is reacted in a first-stage, back-mixed catalytic reactor with a highly dispersed iron-based catalyst having a powder, gel or liquid form. The reactor effluent is pressure-reduced, vapors and light distillate fractions are removed overhead, and the heavier liquid fraction is fed to a second stage back-mixed catalytic reactor. The first and second stage catalytic reactors are operated at 700-850.degree. F. temperature, 1000-3500 psig hydrogen partial pressure and 20-80 lb./hr per ft.sup.3 reactor space velocity. The vapor and light distillates liquid fractions removed from both the first and second stage reactor effluent streams are combined and passed to an in-line, fixed-bed catalytic hydrotreater for heteroatom removal and for producing high quality naphtha and mid-distillate or a full-range distillate product. The remaining separator bottoms liquid fractions are distilled at successive atmospheric and vacuum pressures, low and intermediate-boiling hydrocarbon liquid products are withdrawn, and heavier distillate fractions are recycled and further upgraded to provide additional low-boiling hydrocarbon liquid products. This catalytic multistage hydrogenation process provides improved flexibility for hydroprocessing the various carbonaceous feedstocks and adjusting to desired product structures and for improved economy of operations.