  In this work, we construct and test an analytical and a semianalytical
secular models for two planets locked in a coorbital non-coplanar motion,
comparing some results with the case of restricted three body problem.
  The analytical average model replicates the numerical N-body integrations,
even for moderate eccentricities ($\lesssim$ 0.3) and inclinations
($\lesssim10^\circ$), except for the regions corresponding to quasi-satellite
and Lidov-Kozai configurations. Furthermore, this model is also useful in the
restricted three body problem, assuming very low mass ratio between the
planets. We also describe a four-degree-of-freedom semianalytical model valid
for any type of coorbital configuration in a wide range of eccentricities and
inclinations.
  {Using a N-body integrator, we have found that the phase space of the General
Three Body Problem is different to the restricted case for inclined systems,
and establish the location of the Lidov-Kozai equilibrium configurations
depending on mass ratio. We study the stability of periodic orbits in the
inclined systems, and find that apart from the robust configurations $L_4$,
$AL_4$, and $QS$ is possible to harbour two Earth-like planets in orbits
previously identified as unstable $U$ and also in Euler $L_3$ configurations,
with bounded chaos.
