  Many exo-solar systems discovered in the last decade consist of planets
orbiting in resonant configurations and consequently, their evolution should
show long-term stability. However, due to the mutual planetary interactions a
multi-planet system shows complicated dynamics with mostly chaotic
trajectories. We can determine possible stable configurations by computing
resonant periodic trajectories of the general planar three body problem, which
can be used for modeling a two-planet system. In this work, we review our model
for both the planar and the spatial case. We present families of symmetric
periodic trajectories in various resonances and study their linear horizontal
and vertical stability. We show that around stable periodic orbits there exist
regimes in phase space where regular evolution takes place. Unstable periodic
orbits are associated with the existence of chaos and planetary
destabilization.
