  We generalize classical Yang-Mills theory by extending nonlinear constitutive
equations for Maxwell fields to non-Abelian gauge groups. Such theories may or
may not be Lagrangian. We obtain conditions on the constitutive equations
specifying the Lagrangian case, of which recently-discussed non-Abelian
Born-Infeld theories are particular examples. Some models in our class possess
nontrivial Galilean (c goes to infinity) limits; we determine when such limits
exist, and obtain them explicitly.
