  Neutrino-induced upward-going muons in MACRO have been analysed in terms of
relativity principles violating effects, keeping standard mass-induced
atmospheric neutrino oscillations as the dominant source of nu_mu -> nu_tau
transitions. The data disfavor these exotic possibilities even at a
sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz
invariance violation parameter |Delta v| < 6 * 10^(-24) at sin2theta_v = 0 and
|Delta v| < 2.5--5 * 10^(-26) at sin2theta_v = +/-1. These limits can also be
re-interpreted as upper bounds on the parameters describing violation of the
Equivalence Principle.
