Dynamics of many recently discovered multi-planetary systems is clearly dominated by non-linear interactions and we would expect a priori to find most of them with chaotic behaviors. However, the fact that we observe these planetary systems suggest that they have been in existence for a long time. The lifespan of planetary systems being indeed particularly sensitive to their dynamical structure, what mechanisms keep them stable?

An extrasolar planetary system, even with large masses and eccentricities, can be stable if planetary orbits are close to stable resonant periodic orbits. Indeed, it has been recently confirmed that in most of the multi-planetary systems, the two planets are locked in mean motion resonances (MMR). It has also been recently established by a number of authors (e.g. Chiang & Murray 2002, Lee & Peale 2002) that orbits in almost all multi-planet systems are locked in apsidal secular resonance (ASR), i.e. the longitudes of periapse on average precess at the same rate. The combination of these two types of resonances (MMR & ASR) may provide the key to the solution of the stability problem in extrasolar multi-planetary systems.

There are two types of ASR: aligned and anti-aligned; i.e. the relative apsidal longitude of the two orbits librates about 0 or 180 deg. It appears that both types are present in currently discovered planetary systems. The GJ 876 system has been the first extrasolar planetary system found in aligned apsidal resonance (by Lee & Peale 2002). On the other hand, the HD 82943, HD 12661, and HD 160691 systems are the first three ones found in anti-aligned apsidal resonance (respectively by Ji et al. 2003, Lee & Peale 2003, and Bois et al. 2003). According to Bois et al. (2003), the anti-aligned apsidal topology, combined with MMR, is more wide-ranging than the particular observed cases. It is a promising discovery suitable for a stable regime despite relatively small semimajor axes with respect to the important masses in interaction (high eccentricities also help).

Among the various studied factors of stabilization, the presence of internal resonances to the multiple planet systems proves to be the deciding factor for stability and its preservation. New orbital topologies have been identified with their associated stabilizing mechanisms revealing new resources of orbital resonances. The MMR can be indeed preserved by synchronous precessions of the orbital planes. In these configurations, the relative orientation of the orbits and the starting positions of the planets are such that the planets never experience close encounters.