The vibrational states, absorption energies, and diffusions of H in Pd and Pd 1Ϫx Ag x (0рxр1) have been studied by first-principle calculations. All results compare favorably to experiment. The zero-point motion of H is important in the determination of the H site occupation, in the estimation of the diffusion barrier, and in the explanation of the reversed isotope effect. The interesting anomalous isotope effect is explored, and a diffusion mechanism is proposed for tritium. The preferred diffusion paths of H in Pd and Pd 1Ϫx Ag x are ''indirect'' paths. According to the absorption energies and diffusion barriers, H diffusion in Pd-Ag alloys should avoid the Ag-rich areas.