The relative stabilities of the H2Ge=X, trans-HGeXH, and cis-HGeXH (X = O, S, Se) species and the transition states for H2Ge=Se <-> trans-HGeSeH and trans-HGeSeH <-> cis-HGeSeH isomerizations were investigated using post-Hartree-Fock ab initio methods. Geometry optimization and frequency calculations were performed at the HF, MP2, DFT, and QCISD(T) levels using TZP(2d,2p), TZP(2df,2pd), and TZP++(2df,2pd) basis sets. In the cases of oxygen and sulfur, the isomers H2Ge=O and H2Ge=S represent the structures with the highest energy, and the global minima corresponds to the trans HGeSH and cis-HGeOH forms, respectively. In a more detailed study of the potential energy surface of the Ge[H2Se] system, we have found that the trans-HGeSeH structure is a global minimum separated at the QCISDT/TZP(2df,2pd) level by only 0.5 and 2.0 kcal/mol from H2Ge=Se and cis-HGSeH, respectively. In all cases the electron correlation energy plays a dominant role, and reliable assignment of the relative stability of these energetically close-lying isomers was possible using only higher levels of ab initio theory.