  We introduce and study new integrable models of A_n^{(1)}-Non-Abelian Toda
type which admit U(1)\otimes U(1) charged topological solitons. They correspond
to the symmetry breaking SU(n+1) \to SU(2)\otimes SU(2)\otimes U(1)^{n-2} and
are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY
gauge theory in large n limit.
  It is shown that this family of relativistic IMs corresponds to the first
negative grade q={-1} member of a dyonic hierarchy of generalized cKP type. The
explicit relation between the 1-soliton solutions (and the conserved charges as
well) of the IMs of grades q=-1 and q=2 is found. The properties of the IMs
corresponding to more general symmetry breaking SU(n+1) \to SU(2)^{\otimes
p}\otimes U(1)^{n-p} as well as IM with global SU(2) symmetries are discussed.
