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Recently the space-time configurations of a set of non-threshold boundstates, called the (F, Dp) bound states, have been constructed explicitly forevery $p$ with $2 \le p \le 7$ in both type IIA (for $p$ even) and type IIB(for $p$ odd) string theories by the present authors. By making use of theSL(2, Z) symmetry of type IIB theory we construct a more general SL(2, Z)invariant bound state of the type ((F, D1), (NS5, D5)) in this theory from the(F, D5) bound state. There are actually an infinite number of $(m,n)$ stringsforming bound states with $(m',n')$ 5-branes, where strings lie along one ofthe spatial directions of the 5-branes. By applying T-duality along one of thetransverse directions we also construct the bound state ((F, D2), (KK, D6)) intype IIA string theory. Then we give a list of possible bound states which canbe obtained from these newly constructed bound states by applying T-dualitiesalong the longitudinal directions as well as S-dualities to those in type IIBtheory.Comment: 21 pages LaTeX, no figures, More general charge relation Eq.(2.23) is  given, the text has been revised accordingly, version to appear in Phys. Rev.

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

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>,</mml:mo><mml:mi /></mml:math>D5) bound state, SL(2,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo>)</mml:mo></mml:math>invariance and the descendant states in type IIB and type IIA string theory

(F,D5) bound state, SL(2,Z)invariance and the descendant states in type IIB and type IIA string theory