We explore the stability of extremely low-mass stars (M < 0.25 M⊙) across a wide range of composition, effective temperature, and luminosity. We identify the instability boundaries associated with radial oscillations. These are a strong function of both composition and radial order (0 ≤ n ≤ 13). The classical blue edge shifts to higher effective temperature and luminosity with decreasing hydrogen abundance. Higher-order modes are more easily excited, and small islands of instability develop. Short-period oscillations have been discovered in the low-mass pre-white dwarf component of the eclipsing binary J0247–25. If its envelope is depleted in hydrogen, J0247–25B is unstable to intermediate-order p modes. Driving is by the classical κ mechanism operating in the second helium ionization zone. The observed periods, temperature and luminosity of J0247–25B require an envelope hydrogen abundance 0.2 ≤ X ≤ 0.3.