We present observations from Voyager 1 and 2 of nonthermal ions from H through Fe in the Jovian magnetosphere using the low-energy particle telescope (LEPT), one of the two sensors of the low-energy charge particle (LECP) experiment. At ~1 MeV/nucleon the major constituents of the ion population were H, He, C, O, Na, S, and the hydrogen molecules H2 and H3. Relative to He, the abundance of H and H3 at equal energy/nucleon was highest in the outer magnetosphere, the abundance of O, Na, and S was highest in the inner magnetosphere, and the abundance of C was constant throughout the magnetosphere. He and C may be of largely solar origin, while H2, H3, O, Na, and S are largely of local origin. The variations in abundance ratios were accompained by a general hardening of the energetic particle spectra near 1 MeV/nucleon with decreasing radial distance. We are able to find a parameter &eegr;, assumed to be a species-dependent constant times energy/nucleon, in terms of which the flux ratios among most species do not change with radial distance. These 'invariant' ratios indicate that there are approximately equal numbers of nonthermal O, S, and He ions, with the abundance of H ions being a factor of ~15 higher. The large ratio changes at equal energy/nucleon can then be ascribed to the changing spectral slopes. The parameter &eegr; may be reasonably identified with energy/charge, in which case we are able to deduce relative charge to mass ratios for H, He, C, O, and S. If He is doubly ionized, we find that the nonthermal carbon has an approximate charge state of +6, typical of solar wind particles, while oxygen and sulfur have low charge states (+2 to +4), typical of local plasma sources. Spectral changes over the range of ~30 to ~16 RJ, in this interpretation, are consistent with particle energization by inward radial diffusion conserving the first adiabatic invariant. In the Jovian magnetotail, at the time of the Voyager 2 outpass, the energetic particle population was a combination of Jovian particles with soft spectra and interplanetary particles (probably of solar flare origin) with much harder spectra. Above ~1 MeV/ nucleon the interplanetary particles were dominant . Beyond ~160 RJ, in the 'magnetospheric wind' region, the nonthermal ion intensity increased and reflected an oxygen-and sulfur-rich composition typical of the middle magnetosphere. Two short-lived intensity increases were observed at ~290 RJ which had heavy ion abundance ratios and spectra similar to those found in the inner magnetosphere. The release of these particles was apparently associated with the arrival at Jupiter of a fast solar wind stream.