The hydrogenolysis of carbon-oxygen bonds is an important model reaction in upgrading biomass-derived furanic compounds to transportation fuels. One of these model reactions, namely conversion of 5-hydroxymethylfurfural (HMF) to the gasoline additive 2,5-dimethylfuran (DMF), is especially attractive. In this study, bimetallic Cu-Co catalysts supported on CeO2, ZrO2, and Al2O3 were used for the selective hydrogenolysis of HMF to DMF. The structures of the fresh and used catalysts were studied using X-ray diffraction, the Brunauer-Emmett-Teller method, transmission electron microscopy, temperature-programmed reduction by H2, temperature-programmed desorption of NH3, and CHNS analysis. The structures were correlated with the catalytic activities. The Cu-Co/CeO2 catalyst produced mainly 2,5-bis(hydroxymethyl)furan via reduction of C=O bonds on large Cu particles. The Cu-Co/Al2O3 catalyst gave the best selectivity for DMF, as a result of a combination of highly dispersed Cu, mixed copper-cobalt oxides, and suitable weak acidic sites. Cu-Co/ZrO2 had low selectivity for DMF and produced a combination of various over-hydrogenolysis products, including 2,5-dimethyltetrahydrofuran and 5,5-oxybis(methylene)-bis(2-methylfuran), because of the presence of strong acidic sites. The reaction pathways and effects of various operating parameters, namely temperature, H2 pressure, and time, were studied to enable optimization of the selective conversion of HMF to DMF over the Cu-Co/Al2O3 catalyst.