  The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion
resonances is studied by using the model of the general three body problem in a
rotating frame and by determining families of periodic orbits for each
resonance. Both planar and spatial cases are examined. In the spatial problem,
families of periodic orbits are obtained after analytical continuation of
vertical critical orbits. The linear stability of orbits is also examined.
Concerning initial conditions nearby stable periodic orbits, we obtain
long-term planetary stability, while unstable orbits are associated with
chaotic evolution that destabilizes the planetary system. Stable periodic
orbits are of particular importance in planetary dynamics, since they can host
real planetary systems. We found stable orbits up to $60^\circ$ of mutual
planetary inclination, but in most families, the stability does not exceed
$20^\circ$-$30^\circ$, depending on the planetary mass ratio. Most of these
orbits are very eccentric. Stable inclined circular orbits or orbits of low
eccentricity were found in the $4/3$ and $5/2$ resonance, respectively.
