Reaction pathways for the decomposition of HXGeO (X=H, F, Cl, and Br) on the ground state potential energy surface have been studied using B3LYP and CCSD(T) levels of theory. Five different reaction mechanisms are proposed: (A) 1,1-HX elimination, (B) 1,2-H shift, (C) 1,2-X shift, (D) H and XGeO radicals formation, and (E) X and HGeO radicals formation. From a consideration of the effect of halogen substitution, the following conclusions emerge: (1) Of the pathways leading to the destruction of HXGeO, the lowest energy route is the 1,2-H shift forming the much more stable hydroxygermylene XGeOH. (2) Although not highly stable in a thermodynamic sense, HXGeO itself certainly exists and is found to be kinetically stable with respect to the unimolecular reactions given above. (3) In the case of mono-halogen substitution, HXGeO is more stable than HGeOX (1,2-X shifted isomer), but less stable than XGeOH (1,2-H shifted isomer). Moreover, theoretical investigations suggest that the divalent XGeOH and HGeOX species all have a planar structure in both trans and cis forms. These forms have a small energy difference between them and a low barrier separating them. (4) In the case of halogen-substituted germanones, the heavier the halogen X in HXGeO, the more competitive the 1,1-HX elimination is with the 1,2-H shift. (5) The stabilization energies, which indicate the extent to which the halogen substitution stabilizes the GeO double bond, increase from X=F to Cl to Br to H and show a reasonable linear correlation with the electronegativity of the halogen.