  We study discrete vortices in coupled discrete nonlinear Schrodinger
equations. We focus on the vortex cross configuration that has been
experimentally observed in photorefractive crystals. Stability of the
single-component vortex cross in the anti-continuum limit of small coupling
between lattice nodes is proved. In the vector case, we consider two coupled
configurations of vortex crosses, namely the charge-one vortex in one component
coupled in the other component to either the charge-one vortex (forming a
double-charge vortex) or the charge-negative-one vortex (forming a, so-called,
hidden-charge vortex). We show that both vortex configurations are stable in
the anti-continuum limit if the parameter for the inter-component coupling is
small and both of them are unstable when the coupling parameter is large. In
the marginal case of the discrete two-dimensional Manakov system, the
double-charge vortex is stable while the hidden-charge vortex is linearly
unstable. Analytical predictions are corroborated with numerical observations
that show good agreement near the anti-continuum limit but gradually deviate
for larger couplings between the lattice nodes.
