Self-oscillations on a partially wetted cylindrical catalyst pellet 1% Pd/gamma-Al2O3 in a-methylstyrene (AMS) hydrogenation accompanied by liquid evaporation are studied. By NMR tomography (magnetic resonance microimaging), images of the liquid-phase distribution within the porous pellet are obtained and the liquid-phase redistribution is monitored immediately during the process. The physical mechanism and simplified one-dimensional model are suggested to explain the observed phenomenon. The model predicts well the experimental period (2-3 min) and the amplitudes of the temperature oscillations at the lower (dry) part of the pellet and also the liquid front oscillations at the upper part. The instability mechanism (negative feedback with time lag) is based on complex interaction among the processes of imbibition, evaporation, and gas-phase hydrogenation.