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The currents and the super-operators product expansions of theN = 4 super-Walgebra are obtained. The generators of this extended conformal algebra consistof the stress-tensor superfield J and the primary superfields Φ ± of integer orhalf-integer conformal weight Δ and Cartan–Weylcharge q. The algorithm forderiving the N = 4 super-W algebra is given for particular cases. Explicit formsof the operator product algebra ΦΦ for different values of Δ are given.

The quantization ofN = 2 supersymmetric Yang-Mills theory coupled to a Fayet-Sohnius hypermuttiplet is performed in the harmonic superspace, by requiring BRS and anti-BRS invariances. The corresponding Ward identities and the renormalized BRS and anti-BRS symmetries are derived.