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 .