  We analyze two-component spatial optical vortex solitons supported by
parametric wave mixing processes in a nonlinear bulk medium. We study two
distinct cases of such localised waves, namely, parametric vortex solitons due
to phase-matched second-harmonic generation in an optical medium with competing
quadratic and cubic nonlinear response, and vortex solitons in the presence of
third-harmonic generation in a cubic medium. We find, analytically and
numerically, the structure of two-component vortex solitons, and also
investigate modulational instability of their plane-wave background. In
particular, we predict and analyze in detail novel types of vortex solitons, a
`halo-vortex', consisting of a two-component vortex core surrounded by a bright
ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a
harmonic field that guides a ring-like localized mode of the
fundamental-frequency field.
