Transmission electron energy-loss spectroscopy has been used to follow the positions of the Δ1 and L1 conduction-band minima, and the L3 saddle point, as a function of Ge content in Ge xSi1-x (x=0-0.95) alloys. By analyzing the shape of the Si 2p→conduction-band (CB) spectra we find that L3 and Δ1 shift largely together, as the band-structure compatibility relations predict. L1 shifts rapidly downwards with respect to Δ1 as the Ge content increases. Measurements were carried out in a scanning transmission electron microscope at a spatial resolution of better than 2 nm. Based on these results, this technique can be used to identify the composition of thin GexSi1-x alloys with a precision of better than 5%.