Electron-stimulated desorption (ESD) of hydrogen from GaN(0001) has been observed and characterized using electron-energy-loss spectroscopy. Saturation exposure to atomic hydrogen produces a decrease in the intensity of energy loss peaks at 3.5 and 6.6 eV and an increase in the intensity of loss peaks at 11.7 and 18 eV. Bombardment with 90 eV electrons produces a reversal of the hydrogen-induced changes at 3.5, 6.6, and 11.7 eV. The increased intensity at 18 eV is almost unchanged by electron exposure. We conclude that the reversal of changes at 3.5, 6.6, and 11.7 eV is due to electron-stimulated desorption of hydrogen from Ga sites while the loss peak at 18 eV may be due to bulk hydrogen and not affected by 90 eV electrons. Cross sections for removal of H and D are found to be 2 x 10(-17) and 7 x 10(-18) cm(2), respectively. The large cross section and small isotope effect for ESD of hydrogen from GaN indicates the participation of a long-lived excited electronic state.