  We have investigated the classical stability of magnetically charged black
$p$-brane solutions for string theories that include the case studied by
Gregory and Laflamme. It turns out that the stability behaves very differently
depending on a coupling parameter between dilaton and gauge fields. In the case
of Gregory and Laflamme, it has been known that the black brane instability
decreases monotonically as the charge of black branes increases and finally
disappears at the extremal point. For more general cases we found that, when
the coupling parameter is small, black brane solutions become stable even
before reaching to the extremal point. On the other hand, when the coupling
parameter is large, black branes are always unstable and moreover the
instability does not continue to decrease, but starts to increase again as they
approach to the extremal point. However all extremal black branes are shown to
be stable even in this case. It has also been shown that main features of the
classical stability are in good agreement with the local thermodynamic behavior
of the corresponding black hole system through the Gubser-Mitra conjecture.
Some implications of our results are also discussed.
