The reactions of H atoms with GeH4, GeH3Cl, GeH2Cl2, and GeHCl3 have been studied systematically using ab initio molecular orbital theory. Theoretical analysis provides conclusive evidence that the main process occurring in each case is hydrogen abstraction from the Ge-H bonds. The reaction thermal rate constants for the temperature range 200-3000 K are deduced by canonical variational transition state theory (CVT) with small curvature tunneling (SCT) correction method. The CVT/SCT rate constants exhibit typical non-Arrhenius behavior. Three-parameter rate-temperature formulas have been fitted as follows: k(1) = 3.09 x 10(-17)T(2.16) exp(-286.74/T), k(2) = 1.94 x 10(-17)T(2.18) exp(-276.82/T), k(3) = 4.19 x 10(-18)T(2.37) exp(-227.64/T), and k(4) = 2.02 x 10(-17) T-1.98 exp(-218.51/T) for the reactions of H with GeH4, GeH3Cl, GeH2Cl2, and GeHCl3, respectively (in units Of cm(3) molecule(-1) s(-1)). Studies show that chlorine substitution has a very slight effect on the strength and reactivity of the Ge-H bonds in GeH(4-n)Cln (n = 1-3).