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N=2 supersymmetric Yang--Mills theories coupled to matter are considered inthe Wess--Zumino gauge. The supersymmetries are realized nonlinearly and theanticommutator between two susy charges gives, in addition to translations,gauge transformations and equations of motion. The difficulties hidden in suchan algebraic structure are well known: almost always auxiliary fields can beintroduced in order to put the formalism off--shell, but still the fielddependent gauge transformations give rise to an infinite dimensional algebraquite hard to deal with. However, it is possible to avoid all these problems bycollecting into an unique nilpotent operator all the symmetries defining thetheory, namely ordinary BRS, supersymmetries and translations. According tothis method the role of the auxiliary fields is covered by the external sourcescoupled, as usual, to the nonlinear variations of the quantum fields. Theanalysis is then formally reduced to that of ordinary Yang--Mills theory.Comment: Conclusions changed, refs. adde

OFF-SHELL FORMULATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER WITHOUT AUXILIARY FIELDS