The structures of the anionic germanium Ge-n(-) clusters and the corresponding neutral Ge-n clusters (n=2-6) have been investigated using B3LYP-DFT and CCSD(T) methods. The 6-311+G(3df) basis set is employed for the dimers and trimers, while the smaller 6-311+G(d) basis set is used for clusters with n > 3. The most stable structures for the germanium cluster anions Ge-3(-), Ge-4(-), and Ge-5(-), and Ge-6(-) are found to be C-2 upsilon((2)A(1)), D-2h(B-2(2g)) , D-3h((2)A(2)"), and D-4h((2)A(2u)), respectively. In the case of Ge-2(-), our calculations show that the low lying (2)Pi(u) and (2)Sigma(g)(+) states are within 1 kcal/mol of each other and both states are candidates for the ground state of the anion. The adiabatic electron affinities calculated for the Ge, clusters with n = 2,3,4,6 are within 0.1 eV of the corresponding experimental values. Furthermore, the adiabatic excitation energies computed at the CCSD(T) level for the low lying states of Ge-3 and Ge-4 compare quite well with the assignments of the bands observed in the photoelectron spectra of Ge-3(-) and Ge-4(-) by Burton, Xu, Arnold, and Neumark [J. Chem. Phys. 104, 2757 (1996)].