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We study the Poisson bracket algebra of the $N=2$ supersymmetric chiral WZNWmodel in superspace. It involves two classical r-matrices, one of which comesfrom the geometrical constraints implied by $N=2$ supersymmetry. The phasespace itself consists of superfields satisfying constraints involving thisr-matrix. An attempt is made to relax these constraints. The symmetries of themodel are investigated.Comment: 21 page

N = 2 CHIRAL WZNW MODEL IN SUPERSPACE