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We construct infinite sets of local conserved charges for the conformalaffine Toda model. The technique involves the abelianization of thetwo-dimensional gauge potentials satisfying the zero-curvature form of theequations of motion. We find two infinite sets of chiral charges and apart fromtwo lowest spin charges all the remaining ones do not possess chiral densities.Charges of different chiralities Poisson commute among themselves. We discussthe algebraic properties of these charges and use the fundamental Poissonbracket relation to show that the charges conserved in time are in involution.Connections to other Toda models are established by taking particular limits.Comment: 18 pages, LaTeX, (one appendix and one reference added, small changes  in introduction and conclusions, eqs.(5.14) and (5.19) improved, final  version to appear in Int. J. Modern Phys. A

THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS