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We present a new set of Cepheid, full amplitude, non-linear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical of Cepheids in the Small Magellanic Cloud (SMC) and for stellar masses ranging from 3.25 to 4M_☉. Predicted φ₂₁ 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. 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 logP_SO≥-0.12 and logP_FO≥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 towards 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 fundamental/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-colour (V, V-I) relation to empirical SMC data supplies a distance modulus (DM) of 19.11±0.08mag. The same outcome applies to pure FO Cepheids and FO components in FO/SO Cepheids, and indeed we find DM=19.16±0.19mag. Current distance estimates do not account for, within current uncertainties on photometry and reddening, the so-called short distance scale.