  We investigate the non-resonant, 3-D (spatial) model of the hierarchical
system composed of point-mass stellar (or sub-stellar) binary and a low-mass
companion (a circumbinary planet or a brown dwarf). We take into account the
leading relativistic corrections to the Newtonian gravity. The secular model of
the system relies on the expansion of the perturbing Hamiltonian in terms of
the ratio of semi-major axes $\alpha$, averaged over the mean anomalies. We
found that the low-mass object in a distant orbit may excite large eccentricity
of the inner binary when the mutual inclination of the orbits is larger than
about of 60 deg. This is related to strong instability caused by a phenomenon
which acts similarly to the Lidov-Kozai resonance (LKR). The secular system may
be strongly chaotic and its dynamics unpredictable over the long-term time
scale. Our study shows that in the Jupiter-- or brown dwarf-- mass regime of
the low-massive companion, the restricted model does not properly describe the
long-term dynamics in the vicinity of the LKR. The relativistic correction is
significant for the parametric structure of a few families of stationary
solutions in this problem, in particular, for the direct orbits configurations
(with the mutual inclination less than 90 degrees). We found that the dynamics
of hierarchical systems with small $\alpha \sim 0.01$ may be qualitatively
different in the realm of the Newtonian (classic) and relativistic models. This
holds true even for relatively large masses of the secondaries.
