Hydrodesulfurization (HDS) and hydrodenitrogenation (HDN) of middle distillates over a commercial Ni-Mo/gamma -Al2O3 have been studied under wide operating conditions (340 to 380 degreesC and 38 to 98 atm). A Power Law model was presented to each one of those reactions. The parameters of kinetic equations were estimated solving the ordinary differential equations by the 4(th) order Runge-Kutta-Gill algorithm and Marquardt method for searching the set of kinetic parameters (kinetic constants as well as the order of the reactions). An adiabatic diesel hydrotreating trickle-bed reactor packed with the same catalyst was simulated numerically in order to check up the behavior df this reaction system. One dimensional pseudo-homogeneous model was used in this work. For each feed, the mass and energy balance equations were integrated along the length of the catalytic bed using the 4(th) Runge-Kutta-Gilr method. The performances of two industrial reactors were checked.