  Galileon models arise in certain braneworld scenarios as modifications to
General Relativity, and are also interesting as field theories in their own
right. We show how the galileon model can be naturally generalized to include
local gauge symmetries, by allowing for couplings to Yang-Mills fields. The
resulting theories have at most second order spacetime derivatives in any
representation of the gauge group, thereby avoiding Ostrogradski ghosts. We
also extend the models to include curved space, and show how in that case we
need to include non-minimal couplings between the galileons and the curvature
tensors for the theory to retain its second order nature.
