Do we observe Levy flights in cosmic rays?

We argue that the so called long flying component (LFC) observed in some co smic ray experiments are yet another manifestation of Levy distributions (w ith index q = 1.3), this time of the distribution observation probability o f the depths of starting points of cascades. It means that LFC is governed by the so caned long-tail Levy-like anomalous superdiffusion, a phenomenon frequently encountered in Nature. Its connection with the so called Tsallis 's statistics is also briefly discussed.