Rate coefficients, k, for the gas-phase reactions of Cl atoms and NO3 radicals with 2,3,3,3-tetrafluoropropene, CF3CF=CH2 (HFO-1234yf), and 1,2,3,3,3-pentafluoropropene, (Z)-CF3CF=CHF (HFO-1225ye), are reported. Cl-atom rate coefficients were measured in the fall-off region as a function of temperature (220-380 K) and pressure (50-630 Torr; N-2, 0(2), and synthetic air) using a relative rate method. The measured rate coefficients are well represented by the fall-off parameters k(0)(T) = 6.5 x 10(-28) (T/300)(-6.9) cm(6) molecule(-2) s(-1) and k(infinity)(T) = 7.7 x 10(-11) (T/300)(-0.65) cm(3) molecule(-1) s(-1) for CF3CF=CH2 and k(0)(T) = 3 x 10(-27) (T/300)(-6.5) cm(6) molecule(-2) s(-1) and k(infinity)(T) = 4.15 x 10(-11) (T/300)(-0.5) cm(3) molecule(-1) s(-1) for (Z)-CF3C=CHF with F-c = 0.6. Reaction product yields were measured in the presence of O-2 to be (98 +/- 7)% for CF3C(O)F and (61 +/- 4)% for HC(O)Cl in the CF3CF=CH2 reaction and (108 +/- 8)% for CF3C(O)F and (112 +/- 8)% for HC(O)F in the (Z)-CF3CF=CHF reaction, where the quoted uncertainties are 2 sigma (95% confidence level) and include estimated systematic errors. NO3 reaction rate coefficients were determined using absolute and relative rate methods. Absolute measurements yielded upper limits for both reactions between 233 and 353 K, while the relative rate measurements yielded k(3)(295 K) = (2.6 +/- 0.25) x 10(-17) cm(3) molecule(-1) s(-1) and k(4)(295 K) = (4.2 +/- 0.5) x 10(-18) cm(3) molecule(-1) s(-1) for CF3CF=CH2 and (Z)-CF3CF=CHF, respectively. The Cl-atom reaction with CF3CF=CH2 and (Z)-CF3CF=CHF leads to decreases in their atmospheric lifetimes and global warming potentials and formation of a chlorine-containing product, HC(O)Cl, for CF3CF=CH2. The NO3 reaction has been shown to have a negligible impact on the atmospheric lifetimes of CF3CF=CH2 and (Z)-CF3CF=CHF. The energetics for the reaction of Cl, NO3, and OH with CF3CF=CH2 and (Z)-CF3CF=CHF in the presence of O-2 were investigated using density functional theory (DFT).