  We study noncommutative open string (NCOS) theories realized in string theory
with time-dependent backgrounds. Starting from a noncommutative Yang-Mills
theory (NCYM) with a constant space-space noncommutativity but in a
time-dependent background and making an S-dual transformation, we show that the
resulting theory is an NCOS also in a time-dependent background but now with a
time-dependent time-space noncommutativity and a time-dependent string scale.
The corresponding dual gravity description is also given. A general SL(2,Z)
transformation on the NCYM results in an NCOS with a time-dependent time-space
noncommutativity and a constant space-space noncommutativity, and also in a
time-dependent background.
