The principal objective of this research is to clarify the mechanisms of chemical inhibition of methane-air diffusion flames by CF3Br and CF3H. An experimental, numerical and analytical study is conducted. In inhibited flames at conditions close to flame extinction significant amount of oxygen is found to leak; through the reaction zone. Therefore an asymptotic analysis is performed to characterize the structure and critical conditions of extinction of uninhibited methane-air diffusion flames. Later this analyses is extended to methane-air diffusion flames inhibited with CF3Br. Critical conditions of extinction of the flame are measured over a wide range with agents added to the air stream and to the fuel stream. Numerical calculations with detailed chemistry are performed to calculate the structure and critical conditions of flame extinction. The numerical results are compared with the measurements.