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Currents of the SL(N) WZWN model are constrained so that the remainingsymmetry is a symmetry of constrained currents as well. Such consistencyenables us to study the Poisson structure of constrained SL(N) WZWN modelsproperly. We establish the Poisson brackets which satisfy the Jacobi identitiesowing to the classical Yang-Baxter equation. The Virasoro algebra is shown byusing them. An SL(N) conformal primary is constructed. It satisfies a quadraticalgebra, which might become an exchange algebra by its quantum deformation.

Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra