The possibility that the internal-symmetry group is a consequence of the gauge invariance of a theory (rather than being phenomenologically chosen) is suggested. For a fully unified theory where all interactions are determined by the gauge invariance, this could come about as a consequence of spontaneous (or dynamical) breakdown. Thus the vacuum state after symmetry breakdown may preserve only a subgroup of a larger arbitrary group of the original unbroken equations. The above suggestion appears to be at least partly realized within the framework of gauge supersymmetry where the local gauge invariance determines all interactions via the field equations R/sub A B/ = lambdag/sub A B/, lambda = const. Starting with an arbitrary internal-symmetry group, we obtain general conditions to determine the remaining unbroken symmetry group when the gauge supersymmetry spontaneously breaks to a vacuum state that is invariant under a generalized global supersymmetry. For the case lambda not-equal 0, if one further assumes that the vacuum state preserves parity, these conditions uniquely determine the remaining unbroken internal-symmetry group to be the U(1) gauge group of Maxwell theory (as well as the Einstein general coordinate group). For the case lambda = 0, the internal-symmetry group is only partly determined. However,more » the condition that a spontaneous breakdown occurs automatically causes a violation of parity, and thus affords a natural origin of this phenomenon for weak interactions. The structure of the pseudo-Goldstone bosons of the theory (which are absorbed by the vector mesons of the broken gauge invariances) is determined.« less