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We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Millstheories coupled to matter. A regularization procedure preserving both the BRSinvariance and the supersymmetry is not known yet, therefore it is necessary toadopt the algebraic method of renormalization, which does not rely on anyregularization scheme. The whole analysis is reduced to the solution ofcohomology problems arising from the generalized Slavnov operator whichsummarizes all the symmetries of the model. Besides to unphysicalrenormalizations of the quantum fields, we find that the only coupling constantof $N=2$ SYMs can get quantum corrections. Moreover we prove that all thesymmetries defining the theory are algebraically anomaly--free.Comment: typing error in eq. (A.9) correcte

ALGEBRAIC RENORMALIZATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER