We present a theoretical study of the dynamics of the first few members of the F + alkane -> HF + alkyl family of reactions (alkane = CH4, C2H6, C3H8, and i-C4H10). Quasiclassical trajectories have been propagated employing a reparameterized semiempirical Hamiltonian that was derived in this work based on ab initio information of the global potential-energy surfaces of all reactions studied. The accuracy of the Hamiltonian is probed via comparison of the calculated dynamics properties with experimental results in the F + CH4 -> HF + CH3, F + CD4 -> DF + CD3, and F + C2H6 -> HF + C2H5 reactions. Additional calculations on the F + C3H8 -> HF + C3H7 and F + i-C4H10 -> HF + C4H9 reactions have been analyzed with emphasis on the difference in the dynamics of reactions occurring at primary, secondary, and tertiary sites. We learn that at low collision energies, the amount of energy going into HF vibration increases very slightly along the primary -> secondary -> tertiary sequence. In addition, reactions involving larger alkane molecules tend to channel more energy toward alkyl products at the expense of the rest of the degrees of freedom. Angular distributions are also dependent on the abstraction site, with tertiary abstractions resulting in slightly more backward scattering than reactions at primary sites.