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The structure of the renormalization of the Yang-Mills theories in the light-cone gauge is investigated. It is shown that, despite the appearance of an infinite number of nonlocal divergent terms, the theory can be made finite to any order in the loop expansion by introducing a finite number of renormalization constants. Those constants can be interpreted as coefficients of a canonical transformation of fields and coupling constants in such a way that gauge invariance and unitarity of the renormalized theory are manifestly satisfied. In particular it is shown that the nonlocal structures are completely decoupled from the physical quantities.

We carefully discuss the finiteness of SUSY YM N=4 in the light cone gauge, first at the one loop level by directly exhibiting the relevant terms of the lowest order Green functions and then at any loop order by using a recent treatment of the renormalization of general Yang-Mills theories in the light cone gauge. We point out the existence of a set of divergent Green functions which however do not contribute to observable quantities, thereby recovering consistency with formulations in other gauges.

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