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We discuss the role of convective zones in the treatment of coupled pulsation and convection. In particular, we have investigated behaviors of the convective depth, $ \eta$ , and of the ratio between the convective and total luminosities, $ \gamma_{\rm c}$ . In deep convection, additional fixed points appear, the values of which increase with the depth of zone, and become larger than unity. A diagram of stability criteria derived from the linearized model has been drawn, which shows stable regions fitting each criterion. Then, various flow patterns have been obtained by means of numerical simulations for sets of $ \gamma_{\mathrm{c}}$ and $ \eta$ , and the structure of the mode has been discussed. The results of simulations are shown in tables and figures with a fixed set of parameters other than the set of $ \gamma_{\mathrm{c}}$ and $ \eta$ , which show that deep convective zones cause chaotic solutions and long-period oscillations. Some suggestions are made based on these findings in stellar pulsation within the convective zone.

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