  We discuss type II and type I branes at general ADE type orbifold
singularities. We show that there are new phases of type I or heterotic string
theory in six dimensions, involving extra tensor multiplets, which arise when
small instantons sit on orbifold singularities. The theories with extra tensor
multiplets are explicitly constructed via orientifolds. The world-volume
theories in type IIB or type I five-branes at orbifold singularities lead to
the existence of several infinite classes of six dimensional, interacting,
renormalization group fixed point theories.
