The Voyager 1 spacecraft has detected energetic neutral particles escaping from the magnetospheres of Jupiter and Saturn. These energetic neutrals are created in charge exchange reactions between radiation belt ions and ambient atoms or molecules in the magnetosphere. If the Io torus is assumed to be the dominant Jovian source region for energetic neutrals, the Voyager observations can be used to infer upper limits to the average ion intensities there below about 200 keV. No readily interpretable in-sity measurements are available in the Io torus at these energies. The middle and outer Jovian magnetospheres may also be a significant source of energetic neutrals. At Saturn, the observed neutral particle count rates are too high to be explained by charge exchange between fast protons and H atoms of the Titan torus. Most of the energetic neutrals may be produced by charge exchanges between heavy ions and a neutral cloud containing H2O in Saturn's inner magnetosphere. If so, the Voyager measurements of energetic neutral fluxes would be the first detected emissions from this region of Saturn's magnetosphere.