CF3Br (Halon 1301) and inert gases is useful for their efficient use and for developing new agents. Because of the similarities between unsteady jet diffusion flames formed over the cup burner and uncontrolled fires, it is believed that studies of fire-suppressing agents in the former system could provide valuable information on the behavior of such agents in actual fires. In the present study, suppression characteristics of CO² were investigated in two flame systems: 1) a periodically oscillating, methane-air jet diffusion flame formed over a cup burner, and 2) a steady-state planar flame formed between opposing jets of fuel and air. A detailed chemical-kinetics model having 31 species and 346 elementary-reaction steps was used. Calculations made for the cup burner yielded a flame-flicker frequency of about 10 Hz. The suppression mechanisms promoted by CO² were investigated by adding CO² to the airflow, while maintaining the total flow rate constant, for both the cup-burner and opposed-jet flames. In the cup-burner flame, the addition of CO² reduced the flame temperature to ~1620 K at suppression. Addition of CO² destabilized the flame base, which then moved downstream in search of a new stabilization location. For CO² volume fractions greater than 14.5 %, the flame base moved out of the computational area, as it could not find a stabilization point within this domain. The unsteady flickering motion of the flame and higher concentrations of CO² accelerated this quenching process through blowout. Even for very high concentrations of CO², the calculations did not yield simultaneous quenching of the entire cup-burner flame. On the other hand, the opposed-jet flame was extinguished through the global extinction of flame chemistry. The low-strain (30 s-1) opposed-jet flame extinguished for CO² volume fractions > 16.4 %, while the moderately strained (90 s-1) flame extinguished for volume fractions > 10.4 %. Both the opposed-jet flames extinguished nearly at the same flame temperature (~1580 K), indicating that the extinction limits in these flames are primarily controlled by chemical kinetics.