Parastatistics and gauge symmetries

It is shown that in Green's parafield theory it is possible to construct a unique nonlinear Lagrangian equivalent to the Yang-Mills gauge Lagrangian of $SO(3)$ symmetry. Thus, Greenberg's paraquark hypothesis is not equivalent to the hypothesis of quark color $SU(3)_c$ symmetry. The features of the $SO(3)$ gauge are analyzed and an interesting possibility of its use as an exact subgroup of broken $SU(3)_c$ is pointed out.