  We establish the action of the three-dimensional non-Abelian bosonization
dualities in the presence of a boundary, which supports a non-anomalous
two-dimensional theory. In particular, we generalize a prescriptive method for
assigning duality consistent boundary conditions used originally for Abelian
dualities to dual non-Abelian Chern-Simons-matter theories with $SU$ and $U$
gauge groups and fundamental matter sectors. The cases of single species matter
sectors and those with both scalars and fermions in the dual theories are
considered. Generalization of our methods to $SO$ and $USp$ Chern-Simons
theories is also discussed.
