  Twin-peak quasi-periodic oscillations (QPOs) are observed in several low-mass
X-ray binary systems containing neutron stars (NSs). Timing analysis of X-ray
fluxes of more than dozen of such systems reveals remarkable correlations
between the frequencies of two characteristic peaks present in the power
density spectra. The individual correlations clearly differ, but they roughly
follow a common individual pattern. High values of measured QPO frequencies and
strong modulation of the X-ray flux both suggest that the observed correlations
are connected to orbital motion in the innermost part of an accretion disc.
Several attempts to model these correlations with simple geodesic orbital
models or phenomenological relations have failed in the past. We find and
explore a surprisingly simple analytic relation that reproduces individual
correlations for a group of several sources through a single parameter. When an
additional free parameter is considered within our relation, it well reproduces
the data of a large group of 14 sources. The very existence and form of this
simple relation supports the hypothesis of the orbital origin of QPOs and
provides the key for further development of QPO models. We discuss a possible
physical interpretation of our relation's parameters and their links to
concrete QPO models.
