A comparison has been made between the electrolysis of 0.1 M NaOD and that of 0.1 M NaOH with platinum as the anode and palladium as the cathode. Steady state galvanostatic polarization of palladium in 0.1 M NaOD and 0.1 M NaOH indicates greater cathodic polarization of palladium in heavy water. Steady state permeation currents for the cathodically generated D and H through palladium membranes of thickness 0.025 mm indicate lower values in the case of D than in the case of H. Polarization curves reveal the possibility of the stepwise formation of alpha and beta phases of palladium deuteride and palladium hydride. This observation is more pronounced in the case of the Pd-NaOD system, as indicated by the Tafel slope and exchange current values. The final limiting current density corresponding to H-2 evolution is about 90 mA cm-2 and that of D2 evolution is 30 mA cm-2. These limiting current values incidentally serve as the critical current densities for the formation of the beta-(Pd deuteride) or beta-(Pd hydride) phases. Photomicrographs of palladium cathodes (rods 0.025 mm thick and 4 mm in diameter) after electrolysis in NaOD revealed cluster formation of D around Pd atoms in the lattice, indicating the possible formation of Pd deuteride due to the supersaturation of the Pd lattice with deuterium. Similar photomicrographs for the loading of palladium with hydrogen from NaOH indicates no cluster formation and shows only particulates of hydrogen in palladium, widely distributed. The large cathodic polarization of palladium in NaOD solution, the high diffusion coefficient of D in Pd, the low steady state permeation current of D in Pd, and the clear indication of cluster formation only in the case of deuterium around Pd atoms in the lattice jointly indicate the large amount of solid state confinement of D rather than hydrogen in the Pd lattice, thereby increasing the probability of tunnelling of deuterium atoms. This may be the cause for some of or all the anomalous behaviour of the Pd-NaOD system during electrolysis observed by Fleischmann et al. and by others.