In the frame of density functional theory, the lowest energy structures of Au 32−n Ag n (n=1–31) clusters are discussed by considering the hollow cage-like and space-filling structures. The calculated results show that the hollow cage-like and space-filling structures are competitive in energy. For Au 32−n Ag n clusters with sizes n=1, 2, 5–8, 11, 12, 16, and 18, the hollow cage-like structures are their lowest energy structures. And for the clusters with other sizes, the space-filling structures are the corresponding lowest energy structures. In addition, the Au 31 Ag cluster with the hollow cage-like configuration is found to be highly stable in structure, and even more stable than the icosahedral Au 32 cluster. It believes that the experimentalists are interested in the finding above.