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The renormalization of N=1 Super Yang-Mills theory is analysed in theWess-Zumino gauge, employing the Landau condition. An all orders proof of therenormalizability of the theory is given by means of the AlgebraicRenormalization procedure. Only three renormalization constants are needed,which can be identified with the coupling constant, gauge field and gluinorenormalization. The non-renormalization theorem of the gluon-ghost-antighostvertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills.Moreover, due to the non-linear realization of the supersymmetry in theWess-Zumino gauge, the renormalization factor of the gauge field turns out tobe different from that of the gluino. These features are explicitly checkedthrough a three loop calculation.

Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge