The extinguishment processes of methane–air coflow diffusion flames formed on a cup burner in earth gravity have been investigated experimentally and computationally. As a gaseous fire-extinguishing agent (CO 2, N 2, He, Ar, CF 3H, CF 3Br, or Br 2) was introduced gradually into a coflowing oxidizer stream, the base (edge) of the flame detached from the burner rim, oscillated, and eventually extinguished. This extinguishment occurred via a blowoff process (in which the flame base drifted downstream) rather than the global chemical extinction typical of counterflow diffusion flames. The agent concentration in the oxidizer required for extinguishment was nearly independent of the mean oxidizer velocity over a wide range, exhibiting a plateau region. Numerical simulations with full chemistry revealed the unsteady blowoff process and predicted the minimum extinguishing concentration (MEC) of each agent in good agreement with the measurement. The calculations indicated that flame stabilization at the flame base depended upon diffusion of radicals and heat from the trailing diffusion flame upstream into the peak reactivity spot (i.e., reaction kernel). For physically acting agents, the flame blew off as the trailing diffusion flame temperature decreased to ≈1700 K, at which point the back-diffusion of heat and chain radicals into the flame stabilizing region was sufficiently reduced. Consequently, the relative ranking of inert agent effectiveness depended primarily on the heat capacity of the agent-laden oxidizer. Nonetheless, for helium, the MEC was lower than that of argon (which has the same specific heat). The numerical results showed that addition of helium leads to greater heat losses from the downstream diffusion region of the flame than addition of argon because helium addition raised the thermal conductivity of the gas mixture relative to argon addition. The results highlight the importance of the downstream diffusion flame conditions for supporting the flame stabilization which ultimately occurs at the reaction kernel.