New important applications of copper metal, e.g., in the areas of hydrogen production, fuel cell operation, and spent nuclear fuel disposal, require accurate knowledge of the physical and chemical properties of stable and metastable copper compounds. Among the copper(I) compounds with oxygen and hydrogen, cuprous oxide Cu(2)O is the only one stable and the best studied. Other such compounds are less known (CuH) or totally unknown (CuOH) due to their instability relative to the oxide. Here we combine quantum-mechanical calculations with experimental studies to search for possible compounds of monovalent copper. Cuprous hydride (CuH) and cuprous hydroxide (CuOH) are proved to exist in solid form. We establish the chemical and physical properties of these compounds, thereby filling the existing gaps in our understanding of hydrogen- and oxygen-related phenomena in Cu metal.