The ion-molecule reactions occurring in GeH(4)/NF(3), GeH(4)/SF(6), and GeH(4)/SiF(4) gaseous mixtures have been investigated by ion trap mass spectrometry and ab initio calculations. While the NF(x)(+) (x=1-3) react with GeH(4) mainly by the exothermic charge transfer, the open-shell Ge(+) and GeH(2)(+) undergo the efficient F-atom abstraction from NF(3) and form GeF(+) and F-GeH(2)(+) as the only ionic products. The mechanisms of these two processes are quite similar and involve the formation of the fluorine-coordinated complexes Ge-F-NF(2)(+) and H(2)Ge-F-NF(2)(+), their subsequent crossing to the significantly more stable isomers FGe-NF(2)(+) and F-GeH(2)-NF(2)(+), and the eventual dissociation of these ions into GeF(+) (or F-GeH(2)(+)) and NF(2). The closed-shell GeH(+) and GeH(3)(+) are instead much less reactive towards NF(3), and the only observed process is the less efficient formation of GeF(+) from GeH(+). The theoretical investigation of this unusual H/F exchange reaction suggests the involvement of vibrationally-hot GeH(+). Passing from NF(3) to SF(6) and SiF(4), the average strength of the M-F bond increases from 70 to 79 and 142 kcal mol(-1), and in fact the only process observed by reacting GeH(n)(+) (n=0-3) with SF(6) and SiF(4) is the little efficient F-atom abstraction from SF(6) by Ge(+). Irrespective of the experimental conditions, we did not observe any ionic product of Ge-N, Ge-S, or Ge-Si connectivity. This is in line with the previously observed exclusive formation of GeF(+) from the reaction between Ge(+) and C-F compounds such as CH(3)F. Additionally observed processes include in particular the conceivable formation of the elusive thiohypofluorous acid FSH from the reaction between SF(+) and GeH(4).