  Motivated by the study of non abelian Chern Simons vortices of non
topological type in Gauge Field Theory, we analyse the solvability of planar
Liouville systems of Toda type in presence of singular sources. We identify
necessary and sufficient conditions on the "flux" pair which ensure the radial
solvability of the system. Since the given system includes the (integrable) 2 X
2 Toda system as a particular case, thus we recover the existence result
available in this case. Our method relies on a blow-up analysis, which even in
the radial setting, takes new turns compared with the single equation case.
