  We study the effects of violation of the equivalence principle (VEP) or
violation of Lorentz invariance (LIV) in the neutrino sector on the asymmetry
between T-conjugate oscillation probabilities, $\Delta P_T \equiv
P(\nu_{\alpha} \to \nu_{\beta}) - P(\nu_{\beta} \to \nu_{\alpha})$, in a
three-flavour framework. We find that additional mixing due to these
mechanisms, while obeying all present bounds, can lead to an observable
enhancement, suppression, and/or sign change in $\Delta P_T$ for the preferred
energies and baselines of a neutrino factory. The measurement of this asymmetry
can be used to establish a new upper limit of order $10^{-26}$ on VEP or LIV in
the $(\nu_e, \nu_\mu)$ and $(\nu_e, \nu_\tau)$ sectors.
