We have developed a method for quantifying the flux variability of EGRET high-energy gamma-ray sources. We apply this method to all sources in the Second EGRET Catalog except for the one solar flare. Allowing for a small systematic uncertainty, the phase-averaged flux densities of the pulsars are consistent with being nonvariable. Many identified active galactic nuclei are variable, as expected, and it is likely that the apparent nonvariability of some identified active galactic nuclei results from decreased sensitivity to variability at low fluxes and low latitudes. Populations of both variable and nonvariable unidentified sources are found to be in excess at low Galactic latitudes. While low- flux, nonvariable, unidentified sources could result from errors in the Galactic diffuse model, some higher flux, nonvariable, unidentified sources are likely to be Galactic pulsars. The excess of variable, unidentified sources at low latitudes suggests that either pulsars can produce variable gamma rays under special circumstances, or that a new class of Galactic gamma-ray sources exists.