At high accretion rates, thermal instabilities can be suppressed on neutron stars in low mass X-ray binaries (LMXBs). This opens the possibility for other instabilities to be occurring including nonradial oscillations. I will discuss a theoretical study of g-modes on accreting neutron stars which are steadily burning helium. This will include looking at mode stability and showing how the neutron star's spin alters the mode frequencies and eigenfunctions. The development of these techniques will be useful for studying modes on other types of neutron star envelopes. The pulsational stability of accumulating models may lead to some insight as to how type I X-ray bursts are triggered.