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Abstract.A numerical study of detonations in hydrogenoxygen-argon mixtures containing CF4 or CF3H is presented. Experiments have established the promoting effect of these additives on the detonation velocity. The Chapman-Jouguet model fails to explain the observed behavior and a numerical approach solving the steady equations of the fluid dynamics provides a first grasp of such an unexpected behavior. In this paper, we use a numerical model that solves the unsteady equations of the fluid dynamics to simulate the detonation wave and to predict the stabilized detonation velocity. The chemical model used is a parametric one that takes into account a temperature and composition dependence of the heat capacity. In a serie of one-dimensional calculations, we describe first the numerical ignition of the detonation wave. In particular, we examine the effect of the pressure in the driving gas section of the numerical domain. Then, we examine the influence of the additives on the detonation wave propagating in a mixture of H2/O2/Ar. We compare successfully the results of the modeling to experimental data. The promoting behavior of both fluorocarbons is numerically observed up to about 10% of the additives. Our conclusion is that it is possible to model the overall description of a detonation wave in complex reactive system. Prerequisites are the knowledge of the chemical kinetics to within a reasonable accuracy, robust algorithm for computing the fluid dynamics and attention to coupling.