  Small oscillations of current-carrying string loops around stable equilibrium
positions corresponding to minima of the effective potential in the equatorial
plane of the Kerr black holes are studied using the perturbation method. In the
lowest approximation, two uncoupled harmonic oscillators are obtained that
govern the radial and vertical oscillations; the higher-order terms determine
non-linear phenomena and transition to chaotic motion through quasi-periodic
stages of the oscillatory motion. The radial profiles of frequencies of the
radial and vertical harmonic oscillations that are relevant also in the
quasi-periodic stages of the oscillatory motion are given, and their properties
in dependence on the spin of the black holes and the angular momentum and
tension of the string loops are determined. It is shown that the radial
profiles differ substantially from those corresponding to the radial and
vertical frequencies of the geodetical epicyclic motion; however, they have the
same mass-scaling and their magnitude is of the same order. Therefore, we are
able to demonstrate that assuming relevance of resonant phenomena of the radial
and vertical string-loop oscillations at their frequency ratio 3:2, the
oscillatory frequencies of string loops can be well related to the frequencies
of the twin high-frequency quasi-periodic oscillations (HF QPOs) observed in
the microquasars GRS 1915+105, XTE 1550-564, GRO 1655-40. We can conclude that
oscillating current-carrying string loops have to be considered as one of the
possible explanations of the HF QPOs occurring in the field of compact objects.
