be effective. On the other hand, the lower value of metallicity the lower the $Z$ opacity bump. This crucially weakens instability for the MS and H-shell burning models but it seems to have a negligible effect on the instability on the blue loops, especially when compared to the effect of the effective temperature. In models with $Z \la 0.007$ the instability in the phase before core helium ignition is entirely quenched whereas there are still a lot of unstable modes in the models with very well developed blue loop. The pulsational instability on the blue loops vanishes at $Z\approx 0.004$. The reason for that is a difference in the internal structure resulting from a presence of an inward overshooting from the nonburning zone in the blue-loop models. The main effect of this overshooting is visible during the evolution on the RGB, but there is also a thin zone of overshooting below the ICZ. That leads to enrichment of hydrogen in layers just below the ICZ, which causes a steep increase of the $\mu$-gradient in a thin zone. As a consequence the Brunt-Väisälä frequency, $N^2$, increases as well, what makes trapping of pulsation modes more effective and some of them can 