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We generalize the non-threshold bound state in type IIB supergravity of theform (NS5, D5, D3) constructed by the present authors (in hep-th/0011236) tonon-zero asymptotic value of the axion $(\chi_0$). We identify the decouplinglimits corresponding to both the open D3-brane theory and open D5-brane theoryfor this supergravity solution as expected. However, we do not find anynon-commutative Yang-Mills theory (NCYM) limit for this solution in thepresence of NS5 branes. We then study the $SL(2, Z)$ duality symmetry of typeIIB theory for both OD3-limit and OD5-limit. We find that for OD3 theory, ageneric $SL(2, Z)$ duality always gives another OD3-theory irrespective of thevalue of $\chi_0$ being rational or not. This indicates that OD3-theory isself-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 andthese two theories in this case are related to each other by strong-weakduality 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-theoryis S-dual to the type IIB little string theory.Comment: 21 pages, Revtex, v3: minor corrections and physical meaning of the  parameters $l$ and $\tilde{l}$ is given, version to appear in PR

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

(NS5-brane, D5-brane, D3-brane) bound state, open D3-brane, open D5-brane limits, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SL</mml:mi><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>Z</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>duality

(NS5-brane, D5-brane, D3-brane) bound state, open D3-brane, open D5-brane limits, andSL(2,Z)duality