Kinetic studies of the catalytic hydrogenation of vegetable oils and fatty acid methyl esters in liquid-phase are commonly performed in the framework of the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formalism using the competitive and non-competitive adsorption models, which are certainly extreme. Based on the advanced concepts of multicentered adsorption and semi-competitive adsorption, mechanistic kinetic models including a distinction between occupied-sites and covered-sites by the large molecules of FAMEs were formulated without expressing an opinion a priori on whether the adsorption regime is competitive or non-competitive. The theoretical basis of the advanced kinetic modeling is described and successfully applied to three application examples of increasing complexity, including: (a) the hydrogenation of methyl oleate without cis-trans isomerization distinction, (b) the cis-trans isomerization and hydrogenation of the methyl oleate, and (c) the methyl linoleate hydrogenation including the cis-trans isomerization of the methyl oleate. The kinetic studies were carried out using a Ni/?-Al2O3, at 398, 413, 428 and 443 K, under isobaric conditions at hydrogen pressures of 370, 510, and 650 kPa, in the absence of mass-transport limitation. After model discrimination based on statistical analysis and taking into account the physical meaning of the estimated parameters, semi-competitive adsorption models were found to be more realistic than the classical LHHW competitive and non-competitive ones, mainly because they give additional information indicating that the adsorbed molecules of methyl linoleate and methyl oleate could cover up to 12 and 7 surface sites, respectively. These values are in adequate agreement with those expected from a rough computational simulation and seem to be the most interesting result, since they are factual and unattainable from the classical LHHW approaches.