We study the dynamics of a two-planet system , which evolves being in a 1 / 1 mean motion resonance ( co-orbital motion ) with non-zero mutual inclination . In particular , we examine the existence of bifurcations of periodic orbits from the planar to the spatial case . We find that such bifurcations exist only for planetary mass ratios \rho = \frac { m _ { 2 } } { m _ { 1 } } < 0.0205 . For \rho in the interval 0 < \rho < 0.0205 , we compute the generated families of spatial periodic orbits and their linear stability . These spatial families form bridges , which start and end at the same planar family . Along them the mutual planetary inclination varies . We construct maps of dynamical stability and show the existence of regions of regular orbits in phase space .