  We study two-component spatial optical solitons carrying an angular momentum
and propagating in a self-focusing saturable nonlinear medium. When one of the
components is small, such vector solitons can be viewed as a self-trapped
vortex beam that guides either the fundamental or first-order guided mode, and
they are classified as single- and double-vortex vector solitons. For such
composite vortex beams, we demonstrate that a large-amplitude guided mode can
stabilize the ring-like vortex beam which usually decays due to azimuthal
modulational instability. We identify different types of these vector vortex
solitons and demonstrate both vortex bistability and mutual stabilization
effect.
