  Cobordism of virtual string links on $n$ strands is a combinatorial
generalization of link cobordism. There exists a bijection between virtual
string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$.
This paper also shows that virtual string links up to unwelded equivalence are
classified by those groups. Finally, the related theory of welded string link
cobordism is defined herein and shown to be trivial for string links with one
component.
