We study distances of propagation and the group velocities of the muon neutrinos in the presence of mixing and oscillations assuming that Lorentz invariance holds. Oscillations lead to distortion of the $��_��$ wave packet which, in turn, changes the group velocity and the distance $��_��$ travels. We find that the change of the distance, $d_{osc}$, is proportional to the length of the wave packet, $��_x$, and the oscillation phase, $��_p$, acquired by neutrinos in the $��-$ and $K-$ meson decay tunnel where neutrino wave packet is formed: $d_{osc} \propto ����_p$. Although the distance $d_{osc}$ may effectively correspond to the superluminal motion, the effect is too tiny ($\sim 10^{- 5}$ cm) to be reconciled with the OPERA result. We analyze various possibilities to increase $d_{osc}$ and discuss experimental setups in which $d_{osc}$ (corresponding to the superluminal motion) can reach an observable value $\sim 1$ m.

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