The first high resolution electron energy loss spectroscopy (HREELS) studies of the oxidation and nitridation of germanium surfaces are reported. Both single crystal Ge(111) and disordered surfaces were studied. Surfaces were exposed to H, O[subscript]2, NO, N[subscript]2O, and N, after cleaning in ultra-high vacuum. The Ge surfaces were found to be non-reactive to molecular hydrogen (H[subscript]2) at room temperature. Exposure to atomic hydrogen (H) resulted hydrogen adsorption as demonstrated by the presence of Ge-H vibrational modes. The HREEL spectrum of the native oxide of Ge characteristic of [nu]-GeO[subscript]2 was obtained by heating the oxide to 200°C. Three peaks were observed at 33, 62, and 106 meV for molecular oxygen (O[subscript]2) adsorbed on clean Ge(111) at room temperature. These peaks are indicative of dissociative bonding and a dominant Ge-O-Ge bridge structure. Subsequent hydrogen exposure resulted in a shift of the Ge-H stretch from its isolated value of 247 meV to 267 meV, indicative of a dominant +3 oxidation state. A high density of dangling bonds and defects and deeper oxygen penetration at the amorphous Ge surface result in a dilute bridge structure with a predominant +1 oxidation state for similar exposures. Molecules of N[subscript]2O decompose at the surfaces to desorbed N[subscript]2 molecules and chemisorbed oxygen atoms. In contrast, both oxygen and nitrogen are detected at the surfaces following exposure to NO molecules. Both NO and N[subscript]2O appear to dissociate and bond at the top surface layer. Molecular nitrogen (N[subscript]2) does not react with the Ge surfaces, however, a precursor Ge nitride is observed at room temperature following exposure to nitrogen atoms and ions. Removal of oxygen by heating of the NO-exposed surface to 550°C enabled the identification of the Ge-N vibrational modes. These modes show a structure similar to that of germanium nitride. This spectrum is also identical to that of the N-exposed surface heated to 550°C. Surface phonon modes of the narrow-gap semiconducting compounds Mg[subscript]2Sn, Mg[subscript]2Ge and Mg[subscript]2Si were detected at 29, 32, and 40 meV, respectively. The native oxide of all three show a dominant Mg-O mode at 80 meV. Probable Sn-O, Ge-O, and Si-O modes are also identified. Complete removal of the oxide layer was accomplished only on the Mg[subscript]2Si surface but resulted in no noticeable change in the energy of the surface phonon. Results are compared to the known bulk optical properties of these compounds.