  We present a theoretical investigation on periods and amplitudes of RR Lyrae
pulsators by adopting stellar parameters which cover the range of theoretical
evolutionary expectations. Extensive grids of nonlinear, nonlocal and
time-dependent convective RR Lyrae envelope models have been computed to
investigate the pulsational behavior in both fundamental and first overtone
modes at selected luminosity levels and over an effective temperature range
which covers the whole instability region. Blue and red boundaries for
pulsational instability into the HR diagram are presented for three different
mass values M=0.75, 0.65 and 0.58 solar masses, together with an atlas of full
amplitude theoretical light curves for both fundamental and first overtone
pulsators. Theoretical periods have been combined with theoretical amplitudes
in order to predict the location of the pulsators in the amplitude-period
diagram. Comparison with observational data brings to light what we regard as a
clear indication that the region where both fundamental and first overtone show
a stable limit cycle, is populated by fundamental or first overtone pulsators
in Oosterhoff I and Oosterhoff II clusters respectively. Some evident
mismatches between theory and observation have also been found, and they are
presented and discussed.
