This paper presents evolutionary computations which investigate the theoretical predictions concerning metal rich RR Lyrae pulsators found both in the Galactic field and in the Galactic bulge. The main aim of this investigation is to provide a homogeneous evolutionary context for further analyses concerning the pulsational properties of these evolving structures. In this connection a suitable set of stellar models characterized by two different metal contents, namely Z=0.01 and Z=0.02 were followed through both H and He burning phases. This evolutionary scenario covers the theoretical expectations for pulsating He burning structures with ages ranging from 20 to less than 1 Gyr. For each given assumption about the star metallicity we find that "old" He burning pulsators with ages larger than 2 Gyr have a common behavior, with Z=0.01 pulsators slightly more luminous and more massive than Z=0.02 pulsators. However, as soon as the metallicity increases above the solar value, the luminosity of Horizontal Branch (HB) stars increases again. This effect is a direct consequence of the expected simultaneous increase of both original He and metals. The occurrence of "young" RR Lyrae pulsators is discussed. Hydrogen burning isochrones for the quoted metallicity values are also presented and discussed. Finally, the occurrence of a new "gravonuclear instability" in some HB models during the ignition of He shell burning is discussed.

25 pages, 15 ps figures, 8 in gif format, uses aaspp4.sty and tighten.sty, accepted for publication in ApJ