  We discuss a set of generalized, necessary conditions for non-trivial,
interacting fixed points in six dimensional supersymmetric field theories. We
use string theory to argue for the existence of infinite families of
interacting RG fixed point theories. The theories are based on certain gauge
groups and matter content, which we identify, along with additional tensor
multiplets. They are conjectured to arise in the world-volume of Type I D5
branes at orbifold singularities.
