the lack of convection-pulsation interaction. We use the convective flux freezing approximation which is not adequate in large outer convective zones. We do not study properties of these stars to any further extent in this paper.

![Runs of the Brunt-Väisälä frequency, $\log N^2$ (solid lines) and and the Lamb frequencies, $\log L^2_\ell$, for $\ell=1$ (dashed lines) and $\ell=2$ (dotted lines), as a function of $\log T$, for Model1 (top panel) and Model2 (bottom panel). The scales of $\log T_\mathrm{eff}$ are different to represent the actual temperature profiles of the models.[]{data-label="fig3"}](fig3a.eps "fig:"){width="88mm"} ![Runs of the Brunt-Väisälä frequency, $\log N^2$ (solid lines) and and the Lamb frequencies, $\log L^2_\ell$, for $\ell=1$ (dashed lines) and $\ell=2$ (dotted lines), as a function of $\log T$, for Model1 (top panel) and Model2 (bottom panel). The scales of $\log T_\mathrm{eff}$ are different to represent the actual temperature profiles of the models.[]{data-label="fig3"}](fig3b.eps "fig:"){width="88mm"}

As depicted in Fig.\[fig1\], for $Z=0.01$ and $0.015$ there is a large instability strip that covers models both before and after core helium ignition. A comparison of the top- and central-left panels gives the effect of metallicity. For $Z=0.01$ (top-left panel), the range of effective temperatures that covers unstable models on the blue loop 