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The notion of characteristic Lie algebra of a hyperbolic system of PDE was intro- duced by Leznov, Shabat and Smirnov in 1982 and in the recent years characteris- tic Lie algebras of various hyperbolic systems were actively studied by Zhiber's and Habibullin's schools. We will study the growth of the characteristic Lie algebra for the Klein{Gordon equation u xy=f(u).