Reactions of F2 molecules exhibit unusual features, manifesting in high reactivity of F2 with respect to some closed-shell molecules and low reactivity toward chemically active species, such as halogen and oxygen atoms. The existing data base on the reactions of F2 being rather sparse, kinetic and mechanistic studies (preferably over a wide temperature range) are needed to better understand the nature of the specific reactivity of fluorine molecule. In the present work, reactions of F2 with Br atoms and Br2 have been studied for the first time in an extended temperature range using a discharge flow reactor combined with an electron impact ionization mass spectrometer. The rate constant of the reaction F2 + Br → F +BrF (1) was determined either from kinetics of the reaction product, BrF, formation or from the kinetics of Br consumption in excess of F2: k1 = (4.66 ± 0.93) × 10−11 exp(−(4584 ± 86)/T) cm3 molecule−1 s−1 at T = 300–940 K. The rate constant of the reaction F2 + Br2 → products (2), k2 = (9.23 ± 2.68) × 10−11 exp(−(8373 ± 194)/T) cm3 molecule−1 s−1, was determined in the temperature range 500–958 K by monitoring both reaction product (FBr) formation and F2 consumption kinetics in excess of Br2. The results of the experimental measurements of the yield of FBr (1.02 ± 0.07 at T = 960 K) combined with thermochemical calculations indicate that F+Br2F forming channel of reaction (2) is probably the dominant one, at least, at highest temperature of the study.