  We show how one can estimate the multipole moments of the space-time,
assuming that the quasi-periodic modulations of the X-ray flux (quasi-periodic
oscillations), observed from accreting neutron stars or black holes, are due to
orbital and precession frequencies (relativistic precession model). The
precession frequencies $\Omega_{\rho}$ and $\Omega_z$ can be expressed as
expansions on the orbital frequency $\Omega$, in which the moments enter the
coefficients in a prescribed form. Thus, observations can be fitted to these
expressions in order to evaluate the moments. If the compact object is a
neutron star, constrains can be imposed on the equation of state. The same
analysis can be used for black holes as a test for the validity of the no-hair
theorem. Alternatively, instead of fitting for the moments, observations can be
matched to frequencies calculated from analytic models that are produced so as
to correspond to realistic neutron stars described by various equations of
state. Observations can thus be used to constrain the equation of state and
possibly other physical parameters (mass, rotation, quadrupole, etc.) Some
distinctive features of the frequencies, which become evident by using the
analytic models, are discussed.
