  We study the algebraic renormalization of $N=2$ Supersymmetric Yang--Mills
theories coupled to matter. A regularization procedure preserving both the BRS
invariance and the supersymmetry is not known yet, therefore it is necessary to
adopt the algebraic method of renormalization, which does not rely on any
regularization scheme. The whole analysis is reduced to the solution of
cohomology problems arising from the generalized Slavnov operator which
summarizes all the symmetries of the model. Besides to unphysical
renormalizations of the quantum fields, we find that the only coupling constant
of $N=2$ SYMs can get quantum corrections. Moreover we prove that all the
symmetries defining the theory are algebraically anomaly--free.
