The direct hydrogen abstraction reactions of H atoms with GeH4, GeH3F, GeH2F2, and GeHF3 have been studied systematically using ab initio molecular orbital theory. For all of the reactions, the potential energy surface information has been calculated at the MP2 level with the 6-311 G(2d,p) basis set. Energies along the minimum energy path have been improved by a series of single-point ab initio G2MP2//MP2 calculations. Theoretical analysis provides conclusive evidence that the main process occurring in each case is the hydrogen abstraction from the Ge-H bond; the fluorine abstraction from the Ge-F bond has a higher barrier and is difficult to react. Changes of geometries, generalized normal-mode vibrational frequencies, and potential energies along the reaction path of the reactions are discussed and compared. The reaction thermal rate constants for the temperature range 200-3000 K are deduced by the canonical variational transition-state theory (CVT) with small-curvature tunneling (SCT) correction method. The calculated results show that the variational effect is small and that in the lower-temperature range the small curvature tunneling effect is important for all of the title reactions. The CVT/SCT rate constants exhibit typical non-Arrhenius behavior. Three-parameter rate-temperature formulas have been fitted as follows: k(1) = 1.82 x 10(-17)T(2-16) exp(-282.56/T), k(2) = 3.74 x 10(-18)T(2.09) exp(-368.21/T), k(3) = 2.43 x 10(-20)T(2.29) exp(-412.36/T), and k(4) = 1.38 x 10(-19)T(2.25) exp(-536.54/T) for the reactions of H with GeH4, GeH3F, GeH2F2, and GeHF3, respectively (in units of cm(3) molecule(-1)s(-1)). Studies show that the fluorine substitution has an effect on the strength and reactivity of the Ge-H bond in GeH(4-n)Fn (n = 1-3).