We report a basin-hopping Monte Carlo investigation within the embedded-atom method of the structural and energetic properties of bimetallic ZrCu, ZrAl, and CuAl nanoclusters with 55 and 561 atoms. We found that unary Zr55, Zr561, Cu55, Cu561, Al55, and Al561 systems adopt the well known compact icosahedron (ICO) structure. The excess energy is negative for all systems and compositions, which indicates an energetic preference for the mixing of both chemical species. The ICO structure is preserved if a few atoms of the host system are replaced by different species, however, the composition limit in which the ICO structure is preserved depends on both the host and new chemical species. Using several structural analyses, three classes of structures, namely ideal ICO, nearly ICO, and distorted ICO structures, were identified. As the amounts of both chemical species change towards a more balanced composition, configurations far from the ICO structure arise and the dominant structures are nearly spherical, which indicates a strong minimization of the surface energy by decreasing the number of atoms with lower coordination on the surface. The average bond lengths follow Vegard's law almost exactly for ZrCu and ZrAl, however, this is not the case for CuAl. Furthermore, the radial distribution allowed us to identify the presence of an onion-like behavior in the surface of the 561-atom CuAl nanocluster with the Al atoms located in the outermost surface shell, which can be explained by the lower surface energies of the Al surfaces compared with the Cu surfaces. In ZrCu and ZrAl the radial distribution indicates a nearly homogeneous distribution for the chemical species, however, with a slightly higher concentration of Al atoms on the ZrAl surface, which can also be explained by the lower surface energy.