A study has been made of the structures and stabilities of copper and gold clusters and copper-gold nanoalloy clusters, with up to 56 atoms, modeled by the many-body Gupta potential. For pure copper clusters, the lowest energy structures are found to be based on icosahedral packing, while pure gold clusters tend to form less symmetrical (often amorphous) structures. In a number of cases, the replacement of a single gold atom by copper is found to be sufficient to convert the structure to that of the more symmetrical copper cluster. The lowest energy clusters are generally more difficult to find for the bimetallic clusters than for the pure metallic clusters. due to the presence of homotops (related by permuting Cu and Au atoms), as well as geometrical isomers. The structures of the lowest energy bimetallic clusters exhibit primarily icosahedral packing, with (CuAu)(M) and (CuAu3)(M) clusters tending to form layered structures and (Cu3Au)(M) clusters showing greater Cu-Au mixing,