  We introduce a notion of universality classes for the Gregory-Laflamme
instability and determine, in the supergravity approximation, the stability of
a variety of solutions, including the non-extremal D3-brane, M2-brane, and
M5-brane. These three non-dilatonic branes cross over from instability to
stability at a certain non-extremal mass. Numerical analysis suggests that the
wavelength of the shortest unstable mode diverges as one approaches the
cross-over point from above, with a simple critical exponent which is the same
in all three cases.
