Abstract
We construct Lagrangian theories which are simultaneously invariant under supergauge transformations and under Yang-Mills transformations. The simplest of these turns out to be just the usual theory describing the interaction of a Yang-Mills field with a Majorana spinor belonging to the regular representation of the internal symmetry group. This theory is asymptotically free. Other examples, involving in addition to spinors also scalar and pseudoscalar fields are described. They also are asymptotically free, provided the number of scalar supermultiplets is not too high and supergauge invariance, as expected, is preserved by renormalization.
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