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 $ u_mu$ wave packet which, in turn, changes the group velocity and the distance $ u_mu$ travels. We find that the change of the distance, $d_{osc}$, is proportional to the length of the wave packet, $sigma_x$, and the oscillation phase, $phi_p$, acquired by neutrinos in the $pi-$ and $K-$ meson decay tunnel where neutrino wave packet is formed: $d_{osc} propto sigma phi_p$. 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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