  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.
