We present a new set of Cepheid , full amplitude , nonlinear , convective models which are pulsationally unstable in the second overtone ( SO ) .
Hydrodynamical models were constructed by adopting a chemical composition typical for Cepheids in the Small Magellanic Cloud ( SMC ) and stellar masses ranging from 3.25 to 4 M _ { \odot } .
Predicted \phi _ { 21 } Fourier parameters agree , within current uncertainties , with empirical data for pure first and second overtone variables as well as for first/second overtone ( FO/SO ) double-mode Cepheids collected by Udalski et al .
( 1999a , b ) in the SMC .
On the other hand , predicted I band amplitudes are systematically larger than the observed ones in the short period range , but attain values that are closer to the empirical ones for \log P _ { SO } \geq - 0.12 and \log P _ { FO } \geq 0.1 .
We also find , in agreement with empirical evidence , that the region within which both second and first overtones attain a stable limit cycle widens when moving toward lower luminosities .
Moreover , predicted P _ { SO } / P _ { FO } and P _ { FO } / P _ { F } period ratios agree quite well with empirical period ratios for FO/SO and F/FO double-mode SMC Cepheids .

Interestingly enough , current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators .
In fact , we find that the fit of the predicted Period-Luminosity-Color ( V , V-I ) relation to empirical SMC data supplies a distance modulus of 19.11 \pm 0.08 mag .
The same outcome applies to pure FO Cepheids and FO components in FO/SO Cepheids , and indeed we find DM= 19.16 \pm 0.19 mag .
Current distance estimates do not account for , within current uncertainties on photometry and reddening , the so-called short distance scale .