  We generalize noncommutative gauge theory using Nambu-Poisson structures to
obtain a new type of gauge theory with higher brackets and gauge fields. The
approach is based on covariant coordinates and higher versions of the
Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action,
give its first order expansion in the Nambu-Poisson tensor and relate it to a
Nambu-Poisson matrix model.
