Auger electron spectroscopy (AES) has been used to diagnose the nature of Ge enrichment in the top atomic layers of sputter-deposited films of superconducting Nb3Ge. In films with high Tc's, there is a small oxygen-rich layer of 5-10 Å followed by a layer about 60-70 Å thick in which a pronounced Ge enrichment exists. This segregation layer is much thicker than comparable layers found in other binary alloys and this suggests that thermodynamic considerations are not the only cause of the enrichment. Beneath the layers, the Nb3Ge film is chemically homogeneous as a function of depth with constant Nb/Ge ratio existing up to the interface with the substrate where a Nb enrichment occurs. In films with low Tc's, however, there is a smaller oxygen-rich layer and a thinner Ge-rich layer existing at the top surface. Very thin films sputter deposited under otherwise optimum conditions for producing high transition temperatures have low Tc's and an incompletely formed Ge-rich surface layer. Additional experiments have established that the Ge-rich layer forms during the sputter deposition and its thickness is a function of deposition time. The data have serious implications for the fabrication of tunneling junctions for the purposes of probing the physics of superconductivity in Nb3Ge because the thickness of the Ge-rich layer is about the same as the coherence length. Methods to remove the Ge-rich layer without damaging the underlying film were also investigated, as was the effect of oxidation on the layer. One interesting sidelight of the interpretation of the data is that the Ge-rich layer may stabilize the growth of the high-Tc metastable phase.