Rate coefficients over the temperature range 206–380 K are reported for the gas-phase reaction of OH radicals with 2,3,3,3-tetrafluoropropene (CF₃CFCH₂), k₁(T), and 1,2,3,3,3-pentafluoropropene ((Z)-CF₃CFCHF), k₂(T), which are major components in proposed substitutes for HFC-134a (CF₃CFH₂) in mobile air-conditioning units. Rate coefficients were measured under pseudo-first-order conditions in OH using pulsed-laser photolysis to produce OH and laser-induced fluorescence to detect it. Rate coefficients were found to be independent of pressure between 25 and 600 Torr (He, N₂). For CF₃CFCH₂, the rate coefficients, within the measurement uncertainty, are given by the Arrhenius expression k₁(T) = (1.26 ± 0.11) × 10⁻¹² exp[(−35 ± 10)/T] cm³ molecule⁻¹ s⁻¹ where k₁(296 K) = (1.12 ± 0.09) × 10⁻¹² cm³ molecule⁻¹ s⁻¹. For (Z)-CF₃CFCHF, the rate coefficients are given by the non-Arrhenius expression k₂(T) = (1.6 ± 0.2) × 10⁻¹⁸T² exp[(655 ± 50)/T] cm³ molecule⁻¹ s⁻¹ where k₂(296 K) = (1.29 ± 0.06) × 10⁻¹² cm³ molecule⁻¹ s⁻¹. Over the temperature range most relevant to the atmosphere, 200–300 K, the Arrhenius expression k₂(T) = (7.30 ± 0.7) × 10⁻¹³ exp[(165 ± 20)/T] cm³ molecule⁻¹ s⁻¹ reproduces the measured rate coefficients very well and can be used in atmospheric model calculations. The quoted uncertainties in the rate coefficients are 2σ (95% confidence interval) and include estimated systematic errors. The global warming potentials for CF₃CFCH₂ and (Z)-CF₃CFCHF were calculated to be <4.4 and <3.6, respectively, for the 100 year time horizon using infrared absorption cross sections measured in this work, and atmospheric lifetimes of 12 and 10 days that are based solely on OH reactive loss.