  Many of exoplanetary systems consist of more than one planet and the study of
planetary orbits with respect to their long-term stability is very interesting.
Furthermore, many exoplanets seem to be locked in a mean-motion resonance
(MMR), which offers a phase protection mechanism, so that, even highly
eccentric planets can avoid close encounters. However, the present estimation
of their initial conditions, which may change significantly after obtaining
additional observational data in the future, locate most of the systems in
chaotic regions and consequently, they are destabilized. Hence, dynamical
analysis is imperative for the derivation of proper planetary orbital elements.
We utilize the model of spatial general three body problem, in order to
simulate such resonant systems through the computation of families periodic
orbits. In this way, we can figure out regions in phase space, where the
planets in resonances should be ideally hosted in favour of long-term stability
and therefore, survival. In this review, we summarize our methodology and
showcase the fact that stable resonant planetary systems evolve being exactly
centered at stable periodic orbits. We apply this process to co-orbital motion
and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.
