Non-Abelian Born-Infeld and kappa-symmetry

We define an iterative procedure to obtain a non-Abelian generalization of the Born-Infeld action. This construction is made possible by the use of th e severe restrictions imposed by kappa-symmetry. In this paper we will pres ent all bosonic terms in the action up to terms quartic in the Yang-Mills f ield strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the sym metric trace-prescription. (C) 2001 American Institute of Physics.