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We investigate the Gregory-Laflamme instability for bound states of branes intype II string theory and in M-theory. We examine systems with two differentconstituent branes: for instance, D3-F1 or D4-D0. For the cases in which theGregory-Laflamme instability can occur, we describe the boundary ofthermodynamic stability. We also present an argument for the validity of theCorrelated Stability Conjecture, generalizing earlier work by Reall. We discussthe implications for OM theory and NCOS theory, finding that in both cases,there exists some critical temperature above which the system becomes unstableto clumping of the open strings/membranes.Comment: 21 pages, 1 figure. v2: added an appendix on integrated first la

Instabilities of D-brane bound states and their related theories