The kinetics of the hydrogenation of propylene and methylacetylene have been individually studied in a plug-flow reactor under similar conditions to the industrial tail-end selective hydrogenation of a steam-cracking C-3 cut, using 0.05% Pd/gamma-Al2O3 catalyst. These two reactions represent the two consecutive steps of the actual process in the gas phase. Various homogeneous and heterogeneous models have been derived and compared with the data. The LH-HW and the power-law models have been tested. The power-law models fit the data for both reactions in the operating conditions used. Pseudo-reaction orders of zero for propylene and three for hydrogen for propylene hydrogenation, and orders of zero for methylacetylene and one for hydrogen for methylacetylene hydrogenation, were obtained. Reaction orders obtained for the latter case may also be explained by a LH-HW type model if hydrogen is adsorbed atomically and the hydrogen adsorption is the controlling step of the reaction rate.