  We analyzed vibrational stability of metal-poor low-mass main-sequence stars
due to the $\varepsilon$-mechanism. Since outer convection zones of the
metal-poor stars is limited only to the very outer layers, the uncertainty in
treatment of convection does not affect the result significantly. We found that
the dipole g$_1$- and g$_2$-modes certainly become unstable due to the
$\varepsilon$-mechanism for $Z\la 6\times 10^{-4}$. Besides that, we found that
as the metallicity decreases the mass range of the $\varepsilon$-mechanism
instability extends toward higher mass.
