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We investigate the S-matrix of coset WZW theories such as: Liouville theory, SL(2,R)/U(1) Black Hole model, SL(3) Toda theory, etc. Based on integrability of these theories, we derive equations for the S-matrix functional. We construct some exact solutions, which describe Fock space transition amplitudes. We then show that the general solution allows a special type functional integral representation, which can be used for practical calculations.