  In several fields of Physics, Chemistry and Ecology, some models are
described by Liouville systems. In this article we first prove a uniqueness
result for a Liouville system in $\mathbb R^2$. Then we establish an uniform
estimate for bubbling solutions of a locally defined Liouville system near an
isolated blowup point. The uniqueness result, as well as the local uniform
estimates are crucial ingredients for obtaining a priori estimate, degree
counting formulas and existence results for Liouville systems defined on
Riemann surfaces.
