  The external Hartle-Thorne geometry, which describes the space-time outside a
slowly-rotating compact star, is characterized by the gravitational mass $M$,
angular momentum $J$ and quadrupole moment $Q$ of the star and gives a
convenient description which, for the rotation frequencies of more than 95 % of
known pulsars, is sufficiently accurate for most purposes. We focus here on the
motion of particles in these space-times, presenting a detailed systematic
analysis of the frequency properties of radial and vertical epicyclic motion
and of orbital motion. Our investigation is motivated by X-ray observations of
binary systems containing a rotating neutron star which is accreting matter
from its binary companion. In these systems, twin high-frequency quasi-periodic
oscillations are sometimes observed with a frequency ratio approaching $3:2$ or
$5:4$ and these may be explained by models involving the orbital and epicyclic
frequencies of quasi-circular geodesic motion. In our analysis, we use
realistic equations of state for the stellar matter and proceed in a
self-consistent way, following the Hartle-Thorne approach in calculating both
the corresponding values of $Q$, $M$ and $J$ for the stellar model and the
properties of the surrounding spacetime. Our results are then applied to a
range of geodetical models for QPOs.
  A key feature of our study is that it implements the recently-discovered
universal relations among neutron star parameters so that the results can be
directly used for models with different masses $M$, radii $R$ and rotational
frequencies $f_\mathrm{rot}$.

High Energy Astrophysical Phenomena