The general problem of chemical kinetic flame inhibition is examined by means of a theoretical model. This model combines fluid mechanics, energy transport, and detailed chemical kinetics for the oxidation of methane and methanol, coupled with the elementary reactions of the inhibitor, hydrogen bromide. The effects of the inhibitor on laminar flame structure and flame speed are examined over wide ranges of pressure and equivalence ratio. Computed results are found to agree well with available experimental data. It is found that for the same amount of added inhibitor, lean flames are inhibited more rapidly than stoichiometric and rich flames. The efficiency of inhibition is also found to increase with increasing pressure. These trends apply to both methane-air and methanol-air flames. The kinetic mechanisms affecting the inhibition process have been identified and are found to depend strongly on hydrogen atom balance in the flame and pre-flame regions. At higher pressures recombination reactions involving H atoms further increase the efficiency of inhibition.