  We apply the string-triality\cite{duffetal} to argue the existence of the
string-networks of solitonic T and U-strings in the heterotic theory on T^6, S
and T-strings in IIB on K3 x T^2 and, S and U-strings in IIA on K3 x T^2. We
then show the existence of the above heterotic string networks by analyzing the
supersymmetry property of the supergravity solutions. The consistency of these
networks with supersymmetry in the case of IIA and IIB theories is also argued.
Our results therefore give further evidence in favor of the string-triality in
four dimensions.
