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 v(u) -> v(tau) transitions. The data disfavor these exotic possibilities even at a subdominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter vertical bar Delta v vertical bar < 6 x 10(-24) at sin2 theta(v) = 0 and vertical bar Delta(v)vertical bar < 2.5-5 x 10(-26) at sin 2 theta(v) = +/- 1. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the equivalence principle. (c) 2005 Elsevier B.V. All rights reserved.