  We investigate the Gregory-Laflamme instability for bound states of branes in
type II string theory and in M-theory. We examine systems with two different
constituent branes: for instance, D3-F1 or D4-D0. For the cases in which the
Gregory-Laflamme instability can occur, we describe the boundary of
thermodynamic stability. We also present an argument for the validity of the
Correlated Stability Conjecture, generalizing earlier work by Reall. We discuss
the implications for OM theory and NCOS theory, finding that in both cases,
there exists some critical temperature above which the system becomes unstable
to clumping of the open strings/membranes.
