  The recent discovery of a three-planet extrasolar system of HR 8799 by Marois
et al. is a breakthrough in the field of the direct imaging. This great
achievement raises questions on the formation and dynamical stability of the HR
8799 system, because Keplerian fits to astrometric data are strongly unstable
during ~0.2Myr. We search for stable, self-consistent N-body orbits with the so
called GAMP method that incorporates stability constraints into the
optimization algorithm. Our searches reveal only small regions of stable
motions in the phase space of three-planet, coplanar configurations. Most
likely, if the planetary masses are in 10-Jupiter-mass range, they may be
stable only if the planets are involved in two- or three-body mean motion
resonances (MMRs). We found that 80% systems found by GAMP that survived 30Myr
backwards integrations, eventually become unstable after 100Myr. It could mean
that the HR 8799 system undergo a phase of planet-planet scattering. We test a
hypothesis that the less certain detection of the innermost object is due to a
blending effect. In such a case, two-planet best-fit systems are mostly stable,
on quasi-circular orbits and close to the 5:2 MMR, resembling the
Jupiter-Saturn pair.
