We investigate the modal stability of stellar models at masses and luminosity levels corresponding to post main sequence luminous \delta Scuti pulsators .
The envelope models have been computed at fixed mass value ( M / M _ { \odot } =2.0 ) , luminosity level ( log L / L _ { \odot } =1.7 ) and chemical composition ( Y=0.28 , Z=0.02 ) .
According to a nonlinear approach to radial oscillations the present investigation predicts the occurrence of stable second overtone pulsators for the first time .
More in general , we found that when moving inside the instability strip from lower to higher effective temperatures the models show a stable limit cycle in three different pulsation modes : fundamental , first and second overtone .
The shape of both light and velocity curves are presented and discussed , providing a useful tool for the identification of second overtone pulsators among the known groups of radially pulsating stars .

Comparison with observations shows that our nonlinear , nonlocal and time-dependent convective models provide light curves in agreement with observed values , suggesting that second overtone pulsators have already been observed though misclassified as fundamental pulsators .
In a limited region of the instability strip we also found some models presenting mixed mode features , i.e .
radial pulsators which show a stable limit cycle in more than one pulsational mode .

The period ratios of mixed mode pulsators obtained by perturbing the first and the second overtone radial eigenfunctions are in agreement with observative values .
This result is a crucial point for understanding the pulsation properties of \delta Scuti stars since it provides a sound evidence that these variables during their evolution off the main sequence are pure or mixed mode radial pulsators .
Finally , the physical structure and the dynamical properties of second overtone pulsators are discussed in detail .
The role played by the nodal lines in the destabilization of second overtone pulsators is also pointed out .