The coprocessing of coal with petroleum residues provides an effective route for increasing the use of domestic resources---coal and natural gas---to produce liquid fuels. In addition, the initial step of converting petroleum residues alone by hydrocracking can significantly improve the yield of light fuels from crude oil. Several technologies have been developed and commercialized for hydrocracking residues and the liquefaction of coal. All of these technologies can be improved further, based on concepts that can come from a fundamental research program, and using the ideas developed in engineering studies. This work discusses a suggested 5-year research program to carry out fundamental work and explore ideas. The fundamental research program covers work to discover routes to improve yields and product quality when processing coal and petroleum residues together or separately. The program provides both an effective supplement and complementary bridge to the existing programs on coal processing and heavy oil characterization. The work includes the technical rationale and level of effort recommended to implement the studies in the key areas of: new catalysts, detailed feed and product characterization, new processing concepts, and product quality. 4 figs.