  We study the Poisson bracket algebra of the $N=2$ supersymmetric chiral WZNW
model in superspace. It involves two classical r-matrices, one of which comes
from the geometrical constraints implied by $N=2$ supersymmetry. The phase
space itself consists of superfields satisfying constraints involving this
r-matrix. An attempt is made to relax these constraints. The symmetries of the
model are investigated.
