Ames Research Center plasma analyzer high-resolution ion spectra, obtained during the traversals of Jupiter's magnetosheath by Pioneer 10 and 11, are examined for non-Maxwellian characteristics. Many examples are found of proton velocity distributions that are Maxwellian down to an observational limit set by the relative helium flux. However, clear deviations from a Maxwellian velocity distribution sometimes are observed. Most often, these non-Maxwellian proton velocity distributions seem to be enhanced on the low-energy side of the peak, in comparison with a Maxwellian distribution. Even less often, however, the high-energy side of the peak seems to be enhanced. A different type of non-Maxwellian spectrum is also seen occasionally near the times of bow shock crossings, and it exhibits features of both solar wind and high-temperature magnetosheath proton spectra combined.