  We analyze the existence and stability of two-component vector solitons in
nematic liquid crystals for which one of the components carries angular
momentum and describes a vortex beam. We demonstrate that the nonlocal,
nonlinear response can dramatically enhance the field coupling leading to the
stabilization of the vortex beam when the amplitude of the second beam exceeds
some threshold value. We develop a variational approach to describe this effect
analytically.
