Photofragmentations of a methane molecule adsorbed on Pd and Ni(111) surfaces have been studied by means of density functional theory (DFT) and ab initio molecular orbital calculations. The metal surfaces were represented approximately by finite metal clusters M-n (n = 1, 7, 10). The CH4-3s Rydberg excited state is found to be stabilized by about 2.0 and 1.5 eV through the physisorption on Pd and Ni metal surfaces, respectively. This stabilization can be understood as the results of the electron transfer from adsorbates to metal surfaces through an overlap between the CH4 Rydberg orbital and the metal s orbital. Potential energies of the ground and several excited states for the H3C ... HMn system as functions of the C ... H distance suggest that the charge transfer states lead to the fragmentation of CH4 to CH3 and H. The CH4 photodissociation for Pd and Ni(111) surfaces occurs through a direct excitation and the mechanism is basically the same as what we found for the CH4/Pt(111) system [J. Chem. Phys. 107, 415 (1997)].