  We place several new limits on Lorentz violating effects, which can modify
particles' dispersion relations, by considering the highest energy cosmic rays
observed. Since these are hadrons, this involves considering the partonic
content of such cosmic rays. We get a number of bounds on differences in
maximum propagation speeds, which are typically bounded at the 10^{-21} level,
and on momentum dependent dispersion corrections of the form v = 1 +-
p^2/Lambda^2, which typically bound Lambda > 10^{21} GeV, well above the Planck
scale. For (CPT violating) dispersion correction of the form v = 1 + p/Lambda,
the bounds are up to 15 orders of magnitude beyond the Planck scale.
