  Change of sign of the LNRF-velocity gradient 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 a
"humpy" LNRF-velocity profiles occur just above the marginally stable circular
geodesic and could be related to oscillations of accretion discs. The frequency
of such "hump"-induced oscillations can be identified with the maximal rate of
change of the orbital velocity within the "humpy" profile. Therefore, we
introduce an extended orbital resonance model (EXORM) of quasiperiodic
oscillations (QPOs) assuming non-linear resonant phenomena between oscillations
with the orbital epicyclic frequencies and the humpy frequency defined in a
fully general relativistic way. The EXORM is developed for both Keplerian discs
and perfect-fluid tori where the approximation of oscillations with epicyclic
frequencies is acceptable. Clearly, the EXORM could be applied to the
near-extreme Kerr black hole systems exhibiting relatively complex QPO
frequency patterns. Assuming a Keplerian disc, it can be shown that in the
framework of the EXORM, all the QPOs observed in the microquasar GRS 1915+105
could be explained, while it is not possible in the case of QPOs observed in
the Galactic Centre source Sgr A*.
