  Sensitive tests of Lorentz invariance can emerge from the study of neutrino
oscillations, particularly for atmospheric neutrinos where the effect is
conveniently near-maximal and has been observed over a wide range of energies.
We assume these oscillations to be described in terms of two neutrinos with
different masses and (possibly) different maximal attainable velocities (MAVs).
It suffices to examine limiting cases in which neutrino velocity eigenstates
coincide with either their mass or flavor eigenstates. We display the modified
mu to tau neutrino transition probability for each case. Data on atmospheric
neutrino oscillations at the highest observed energies and pathlengths can
yield constraints on neutrino MAV differences (i.e., tests of special
relativity) more restrictive than any that have been obtained to date on
analogous Lorentz-violating parameters in other sectors of particle physics.
