The kinetic modeling of the hydrodesulfurization (HDS) process is based upon the detailed reaction network, distinguishes between the hydrogenolysis- and hydrogenation-steps and accounts for the adsorption of the various reacting species on two types of active sites. The functional form of the rate equations for the conversion of thiophene, (substituted) benzothiophene, (substituted) dibenzothiophene on Co/Mo-alumina appears to be identical. The nature of the active sites, the synergetic effect of Co-sulfides on the activity and the interconversion of sites by hydrogen and hydrogen sulfide are discussed. The application of rate equations accounting explicitly for the in situ conditioning of the catalyst and the HDS is illustrated for thiophene conversion. In the kinetic modeling of HDS of complex mixtures like light cycle oil, containing hundreds of S-components, the structural contribution approach is introduced to reduce the number of independent rate parameters. The structural contributions multiply the rate and adsorption parameters of the parent (unsubstituted) molecules and express the effect of the substituents. Their values were determined from experimental data. Commercial reactor operation for HDS of a complex mixture was simulated, including the effects of external and internal diffusion limitations. An example illustrates the gain that can be achieved in the removal of some of the most refractory S-components by intermediate flashing of H2S. (C) 2004 Elsevier B.V. All rights reserved.