An analysis of EGRET gamma-ray data from the Compton Gamma Ray Observatory, together with data at other wavelengths, leads us to suggest that there are spectral variations of the proton component over the local Galaxy (within several hundred parsec of the Sun); most notably that the spectra are steeper in the Galactic interarm regions. The origin of the variations, if indeed they are substantiated, could be a combination of energetically- and spatially-variable diffusion properties and reacceleration of cosmic-ray particles.