  This letter describes a completely-integrable system of Yang-Mills-Higgs
equations which generalizes the Hitchin equations on a Riemann surface to
arbitrary k-dimensional complex manifolds. The system arises as a dimensional
reduction of a set of integrable Yang-Mills equations in 4k real dimensions.
Our integrable system implies other generalizations such as the Simpson
equations and the non-abelian Seiberg-Witten equations. Some simple solutions
in the k=2 case are described.
