  A class of new nonabelian gauge theories for vector fields on three manifolds
is presented. The theories describe a generalization of three-dimensional
Yang-Mills theory featuring a novel nonlinear gauge symmetry and field
equations for Lie-algebra valued vector potential fields. The nonlinear form of
the gauge symmetry and field equations relies on the vector cross-product and
vector curl operator available only in three dimensions and makes use of an
auxiliary Lie bracket together with the Lie bracket used in Yang-Mills theory.
A gauge covariant formulation of the new theories is given which utilizes the
covariant derivative and curvature from the geometrical formulation of
Yang-Mills theory. Further features of the new theories are discussed.
