  For singular mean field equations defined on a compact Riemann surface, we
prove the uniqueness of bubbling solutions if some blowup points coincide with
bubbling sources. If the strength of the bubbling sources at blowup points are
not multiple of $4\pi$ we prove that bubbling solutions are unique under
non-degeneracy assumptions. This work extends a previous work of Bartolucci,
et, al \cite{bart-4}.
