The structures of N-2, NO, and CO molecules coordinated to the Pd-n (n = 1, 2, 5, 25) clusters as a model of Pd(110) surface were investigated by means of ab initio MO methods. All three molecules, N-2, NO, and CO, coordinate to the one Pd atom by the end-on mode, where the tilted end-on structure is more favorable for NO due to the additional electron in the pi* orbital. On the contrary, in the Pd-2 system, N-2 coordinates to the bridge site of Pd-2 cluster preferably by the side-on mode as reported previously (Blomberg et al. Chem. Phys. Lett. 1991, 179, 524-530), although NO and CO prefer the end-on structure. On the other hand, on the hollow site of the Pd-5 cluster which is the (1 x 1) surface unit of Pd(110) with one Pd atom in the second layer, the tilted structures with an unconventional coordination mode with the interaction of the admolecule with the Pd atoms in both first and second layers were found for all three molecules. With the further extension of the cluster model from the Pd-5 cluster to the Pd-25 of the (3 x 3) surface unit of Pd(110) including Pd atoms up to the third layer, it was suggested that the nonpolar N-2 and polar CO molecules favorably coordinate to the top and the short-bridge sites, respectively, by the end-on mode in agreement with the experimental finding. Those coordination structures and site preferences are discussed in terms of the electron donation and back-donation between the Pd atoms and N-2, NO, and CO molecules.