  We compute the non-abelian couplings in the Chern-Simons action for a set of
coinciding fundamental strings in both the type IIA and type IIB Matrix string
theories. Starting from Matrix theory in a weakly curved background, we
construct the linear couplings of closed string fields to type IIA Matrix
strings. Further dualities give a type IIB Matrix string theory and a type IIA
theory of Matrix strings with winding.
