The authors study the electronic structure of fluorinated and hydrogenated amorphous germanium using a linear combination of atomic orbitals. All the nearest-neighbour and the F-F or H-H second neighbour interactions are considered. The interaction integrals for the Ge-H or (Ge-F) bonds are determined by using a 1/d2 law, d being the bond length. The calculated energies for the various molecular orbitals of GeH4 compare very well with the availability experimental data. The local density of states at H(F) and Ge atoms has been computed both for the s and p orbitals. For a-Ge:H alloys, the computed peaks occur at -10.4 and -3.5 eV for the GeH unit, at -10.3, -4.9 and -2.5 eV for GeH2 and at -10.6, -4.9 and -2.3 eV for GeH3. The peaks near -10 and -2.4 eV originate from the s-like and p-like states of the germanium matrix, respectively. The hydrogen-induced peaks are at -3.5 and -4.9 eV. A reduction in the electronic states is observed near the top of the valence band. For a-Ge:F alloys, the authors obtain fluorine-induced peaks at -12.4 and -10.1 eV for GeF, at -12.9, -10.7, -10.0, -9.5 and -9.2 eV for GeF2 and at -13.3, -11.1, -10.6, -9.9, -9,4 and -8.8 eV for GeF3. Again, a large reduction in the electron states near the top of the valence band is observed. The electronic spectra arising from the simple GeFnHm units, and the (GeFH)n chain-like configurations in amorphous germanium are also given. In these the locations of the peaks induced by fluorine atoms remain undisturbed by the incorporation of hydrogen atoms. However, the positions of the hydrogen-induced peaks are altered significantly by the presence of the fluorine atoms. These results are in reasonable agreement with the available photoemission data. However, more careful photoemission measurements on these alloys need to be performed to detect the predicted electronic structure.