The energy spectrum of neutrino-induced upward-going muons in MACRO has been analysed in terms of relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of $��_�� \to ��_��$ 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 $|��v| < 6 \times 10^{-24}$ at $\sin 2��_v$ = 0 and $|��v| < 2.5 ��5 \times 10^{-26}$ at $\sin 2��_v$ = $\pm$1. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the Equivalence Principle.

3 pages, 2 figures. Presented at NOW 2006: Neutrino Oscillation Workshop, Conca Specchiulla, Otranto, Italy, Sep 2006. To be published in Nucl. Phys. B (Proc. Suppl.)