This paper shows how the study of surpluses of structure is an interesting philosophical task. In particular I explore how local gauge symmetry in quantized Yang-Mills theories is the by-product of the specific dynamical structure of interaction. It is shown how in non relativistic quantum mechanics gauge symmetry corresponds to the freedom to locally define global features of gauge potentials. Also discussed is how in quantum field theory local gauge symmetry is replaced by BRST symmetry. This last symmetry is apparently (...) the result of the fact that we do not know how to define quantum Yang-Mills theories without unphysical gauge boson states. Since Yang-Mills theories describe successfully three of the four fundamental interactions the elucidation of this symmetry is a pressing philosophical question. (shrink)