We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL2n(ℝ) and Spn(ℝ). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements of the W-algebras are presented. © 2003 Elsevier Science B.V. All rights reserved.
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