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Using the Algebraic Bethe Ansatz we consider the correlation functions of theintegrable higher spin chains. We apply a method recently developed for thespin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverseproblem. We construct a representation for the correlation functions on afinite chain for arbitrary spin. Then we show how the string solutions of theBethe equations can be considered in the framework of this approach in thethermodynamic limit. Finally, a multiple integral representation for the spin 1zero temperature correlation functions is obtained in the thermodynamic limit.Comment: LaTeX, 23 pages, replaced with a revised versio

Correlation functions of the higher spinXXXchains