  Gauge theories on a space-time that is deformed by the Moyal-Weyl product are
constructed by twisting the coproduct for gauge transformations. This way a
deformed Leibniz rule is obtained, which is used to construct gauge invariant
quantities. The connection will be enveloping algebra valued in a particular
representation of the Lie algebra. This gives rise to additional fields, which
couple only weakly via the deformation parameter and reduce in the commutative
limit to free fields. Consistent field equations that lead to conservation laws
are derived and some properties of such theories are discussed.
