  The Rossi X-ray Timing Explorer has detected nearly coherent oscillations in
the tails of type I X-ray bursts from 17 low-mass X-ray binaries. The
oscillations are thought to be generated by brightness fluctuations associated
with a surface mode on the rotating neutron star. The mechanism that drives the
modes is, however, not understood, since the burning layer is stable to thermal
perturbations. We show here via a linear perturbation analysis that, even under
conditions when pure thermal perturbations are stable, nonradial surface modes
may still be unstable by the epsilon mechanism. Specifically, we find that, if
helium-burning reactions supply a reasonable fraction of the outgoing flux
during burst decay, nonradial surface modes will grow in time. On the other
hand, the same modes are likely to be stable in the presence of hydrogen
burning via the rp-process. The results naturally explain why oscillations in
the decay phase of type I X-ray bursts are detected only from short-duration
bursts.
