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Change of sign of the velocity gradient (mesured with respect to locally non-rotating frames) has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a>0.9953 for Keplerian discs and a>0.99979 for marginally stable thick discs. Such ``humpy''orbital velocity profiles occur close to but above the marginally stable circular geodesic of the black hole spacetimes. The maximal positive rate of change of the orbital velocity in terms of the proper radial distance introduces a locally defined critical frequency characterizing any processes in the disc capable to excite possible oscillations connected with the velocity hump.