  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
solar masses. 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. 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. Finnaly, current models support the
evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good
distance indicators.
