We report on a numerical investigation on the dynamics and the structure of strained, non-premixed and premixed, H2/NO/F2 flames. This is an important, hypergolic reacting system that has been used in high-power chemical-laser systems and, presently, relied upon in experimental studies of high-speed, supersonic and subsonic, turbulent shear-layer mixing and combustion. The study included a detailed description of the chemical kinetics and molecular transport for the H2/NO/F2 system and was conducted for a wide range of reactant concentrations and inert dilutents, with flow/chemical parameters chosen to correspond to specific chemically reacting, supersonic mixing-layer experiments. Both non-premixed and premixed flames were studied using opposed-jet flow configurations. The results confirmed the experimental conclusion that, even at low reactant concentrations, the H2/NO/F2 system can sustain Damkohler number chemical activity at high strain rates with room-temperature free streams. A comparison between the results of the present numerical simulations and the experimental chemically reacting mixing-layer studies, however, indicates that the predominant fraction of product formation in high-speed, turbulent, mixing layers must take place in a mode in which the reactants are in premixed, rather than in non-premixed, strained diffusion flames.