  The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the
X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among
other ideas, it has been suggested that a non-linear resonance between two
oscillation modes in an accretion disc orbiting either a black hole or a
neutron star plays a role in exciting the observed modulation. Several possible
resonances have been discussed. A particular model assumes resonances in which
the disc-oscillation modes have the eigenfrequencies equal to the radial and
vertical epicyclic frequencies of geodesic orbital motion. This model has been
discussed for black hole microquasar sources as well as for a group of neutron
star sources. Assuming several neutron (strange) star equations of state and
Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies
expected from the model to those observed. Our comparison implies that the
inferred neutron star radius "RNS" is larger than the related radius of the
marginally stable circular orbit "rms" for nuclear matter equations of state
and spin frequencies up to 800Hz. For the same range of spin and a strange star
(MIT) equation of state, the inferrred radius RNS is roughly equal to rms. The
Paczynski modulation mechanism considered within the model requires that RNS <
rms. However, we find this condition to be fulfilled only for the strange
matter equation of state, masses below one solar mass, and spin frequencies
above 800Hz. This result most likely falsifies the postulation of the neutron
star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic
radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes
could stay among the possible choices only if a fairly non-geodesic accretion
flow is assumed, or if a different modulation mechanism operates.
