On type II NS - five-branes in the presence of an R R field

In this letter we use Type II NS5-branes in the presence of an RR field atthe decoupling limit to study a non-commutative version of little stringtheory. We shall see that the decoupling limit of NS5-branes in the presence ofan RR field is completely different from the one we had in ordinary littlestring theory; in particular for Type IIA NS5-branes this decoupling limit canbe defined only when the theory is wrapped on a circle, but nevertheless flowsto the ordinary non-compact (0,2) theory at the IR limit. We also see thatthese theories, in the UV regime, where the non-commutative effects areimportant, can be described by smeared ordinary D3(D2)-branes in Type IIB(A)string theory.