  We investigate the evolutionary behavior of stellar structures with
metallicity Z=0.04 in order to disclose theoretical expectations for both
evolutionary and pulsational behaviors of Super-Metal-Rich (SMR) objects, which
are found in the solar neighborhood, in the Galactic bulge and in elliptical
galaxies. We find that at the exhaustion of central helium SMR stars definitely
undergo the gravonuclear instabilities previously found in some He burning
structures with solar metallicity (Bono et al. 1997b). On the basis of the
evolutionary scenario, we investigate the expected pulsational behavior of He
burning SMR stars for suitable assumptions on the pulsators evolutionary
parameters. Nonlinear, nonlocal, and time-dependent convective models are
discussed, the modal stability is investigated for the first two modes, and the
theoretical predictions about the period distribution inside the instability
strip and the shape of both light and velocity curves are presented. Full
amplitude, nonlinear envelope models show that the range of effective
temperatures where SMR RR Lyrae variables present a stable limit cycle is
smaller in comparison with pulsators characterized by lower metal abundances.
We show that both periods and light curves of different groups of type II
Cepheids with periods shorter than six days, presented by Diethelm (1983,1990),
can be all reproduced by suitable variations in the effective temperature or in
the luminosity level of our SMR post-HB models, supporting evidence of a
substantial homogeneity of these variable.
