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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.doi:10.1017/s1743921313014877 fatcat:4gnv2knbengshoa653tsue74bi