  We generalize the non-threshold bound state in type IIB supergravity of the
form (NS5, D5, D3) constructed by the present authors (in hep-th/0011236) to
non-zero asymptotic value of the axion $(\chi_0$). We identify the decoupling
limits corresponding to both the open D3-brane theory and open D5-brane theory
for this supergravity solution as expected. However, we do not find any
non-commutative Yang-Mills theory (NCYM) limit for this solution in the
presence of NS5 branes. We then study the $SL(2, Z)$ duality symmetry of type
IIB theory for both OD3-limit and OD5-limit. We find that for OD3 theory, a
generic $SL(2, Z)$ duality always gives another OD3-theory irrespective of the
value of $\chi_0$ being rational or not. This indicates that OD3-theory is
self-dual. But, under a special set of $SL(2, Z)$ transformations for which
$\chi_0$ is rational OD3-theory goes over to a 5+1 dimensional NCYM theory and
these two theories in this case are related to each other by strong-weak
duality symmetry. On the other hand, for OD5-theory, a generic $SL(2, Z)$
duality gives another OD5-theory if $\chi_0$ is irrational, but when $\chi_0$
is rational it gives the little string theory limit indicating that OD5-theory
is S-dual to the type IIB little string theory.
