A kinetic model for flame inhibition by antimony-halogen compounds in hydrocarbon flames is developed. Thermodynamic data for the relevant species are assembled from the literature, and calculations are performed for a large set of additional species of Sb-Br-C-H-O system. The main Sb- and Br-containing species in the combustion products and reaction zone are determined using flame equilibrium calculations with a set of possible Sb-Br-C-H-O species, and these are used to develop the species and reactions in a detailed kinetic model for antimony flame inhibition. The complete thermodynamic data set and kinetic mechanism are presented. Laminar burning velocity simulations are used to validate the mechanism against available data in the literature, as well as to explore the relative performance of the antimony-halogen compounds. Further analysis of the premixed flame simulations has unraveled the catalytic radical recombination cycle of antimony. It includes (primarily) the species Sb, SbO, SbO2, and HOSbO, and the reactions: Sb + O + M=SbO + M; Sb + O-2 + M=SbO2 + M; SbO + H=Sb + OH; SbO + O=Sb + O-2; SbO + OH + M=HOSbO + M; SbO2 + H2O=HOSbO + OH; HOSbO + H=SbO + H2O; SbO + O + M=SbO2 + M. The inhibition cycles of antimony are shown to be more effective than those of bromine, and intermediate between the highly effective agents CF3Br and trimethylphosphate. Preliminary examination of a Sb/Br gas-phase system did not show synergism in the gas-phase catalytic cycles (i.e., they acted essentially independently).