  We extend the analysis of the canonical structure of the Wess-Zumino-Witten
theory to the bulk and boundary coset G/H models. The phase spaces of the coset
theories in the closed and in the open geometry appear to coincide with those
of a double Chern-Simons theory on two different 3-manifolds. In particular, we
obtain an explicit description of the canonical structure of the boundary G/G
coset theory. The latter may be easily quantized leading to an example of a
two-dimensional topological boundary field theory.
