The structure, stability, and thermochemistry of various Ge3Hn- isomers (n = 0-5) and of their neutral analogues have been investigated at the B3LYP/6-311+G(d), MP2(full)/6-31G(d), and Gaussian-2 (G2) level of theory. For Ge3H-, both the B3LYP and the G2/MP2 methods predict the cyclic, H-bridged structure 1a(-) as the global minimum, more stable than another cyclic isomer and an open-chain isomer by ca. 10 and 25 kcal mol(-1), respectively. For Ge3H2-, the B3LYP and the G2/MP2 methods provide a somewhat different description of the potential energy surface. At the G2/MP2 level of theory, the global minimum is the cyclic, H2Ge-bridged structure 2a(-), separated by other three nearly degenerate isomers by ca. 10 kcal mol(-1). On the other hand, at the B3LYP level of theory, the cyclic, H-bridged structure 2e(-), not located at the MP2 level of theory, is more stable than 2a(-) by ca. 1 kcal mol(-1). For Ge3H3-, both the B3LYP and the G2/MP2 methods predict the cyclic, H3Ge-bridged isomer 3a(-) as the global minimum, but the energy differences with the other five located isomeric structures predicted by the two methods are quantitatively different. Similar to Ge3H2-, the B3LYP and the G2/MP2 theoretical levels provide a somewhat different description of the Ge3H4- potential energy surface. At the G2/MP2 level of theory, the global minimum is the cyclic structure 4b(-) of C-2V symmetry, featuring a Ge2H4 moiety and a Ge-bridged atom, which is more stable than other three located isomers by 3, 9, and 17 kcal mol-1. On the other hand, at the B3LYP level of theory, the open-chain isomer 4a(-) of H3Ge-Ge-GeH- connectivity is more stable than 4b(-) by ca. 1 kcal mol(-1) and nearly degenerate with the alternative open-chain isomer H3Ge-GeH-Ge-. For Ge3H5-, both the B3LYP and the G2/MP2 methods predict the 2-propenyl-like isomer H3Ge-Ge-GeH2-as the global minimum, with energy differences with other four isomeric structures which range from ca. 1-2 to 13-17 kcal mol(-1). At the G2 level of theory and 298.15 K, the electron affinities of Ge3Hn are computed as 2.17 (n = 0), 2.57 (n = 1), 1.70 (n = 2), 2.41 (n = 3), 2.07/1.80 (n = 4), and 2.71/2.46 eV (n = 5). The two alternative values reported for Ge3H4 and Ge3H5 reflect the alternative conceivable choice for the structure of the involved neutrals and ions. The G2 enthalpies of formation of Ge3Hn and Ge3Hn- (n = 0-5) have also been calculated using the atomization procedure. Finally, we have briefly discussed the implications of our calculations for previously performed mass spectrometric experiments on the negative ion chemistry of GeH4.