  In this paper we make an SL(2,Z)-covariant generalisation of the
noncommutative theories, NCYM and NCOS on the D3-brane, and NCOS on the
D5-brane in type IIB. Usually, the noncommutative theories are obtained by
studying perturbative F-string theory, and the parameters governing the
noncommutative theories are given by the open string data. The S-duality of
NCYM and NCOS on the D3-brane has been seen by dualising the background,
keeping the F-string under study fixed. We give an SL(2,Z)-covariant
generalisation of the open string data relevant when one instead studies
perturbative (p,q)-string theory. The S-duality of NCYM and NCOS on the
D3-brane is reproduced by instead keeping the background fixed and studying
different (p,q)-string theories. We also obtain new noncommutative open
(p,q)-string theories on the D3-brane and the D5-brane which are S-dual to
ordinary NCOS. The theories are studied using the supergravity duals of the
D3-brane and the D5-brane, corresponding to a probe brane in the relevant
background.
