A robust classification of Cepheids into their different sub-classes and, in particular, between classical and Type II Cepheids, is necessary to properly calibrate the period-luminosity relations and for populations studies in the Galactic disc. Type II Cepheids are, however, very diverse, and classifications based either on intrinsic (period, light curve) or external parameters (e.g., [Fe/H], |z|) do not provide a unique classification. We want to ascertain the classification of two Cepheids, HQ Car and DD Vel, that are sometimes classified as classical Cepheids and sometimes as Type II Cepheids. To achieve this goal, we examine both their chemical composition and the presence of specific features in their spectra. We find emission features in the H{alpha} and in the 5875.64 {AA} He I lines that are typical of W Vir stars. The [Na/Fe] (or [Na/Zn]) abundances are typical of thick-disc stars, while BL Her stars are Na-overabundant ([Na/Fe]>+0.5 dex). Finally, the two Cepheids show a possible (HQ Car) or probable (DD Vel) signature of mild dust-gas separation that is usually observed only in long-period type II Cepheids and RV Tau stars. These findings clearly indicate that HQ Car and DD Vel are both Type II Cepheids from the W Vir sub-class. Several studies have reported an increase in the Cepheids abundance dispersion towards the outer (thin) disc. A detailed inspection of the Cepheid classification, in particular for those located in the outer disc, will indicate whether this feature is real or simply an artefact of the inclusion of type II Cepheids belonging to the thick disc in the current samples.
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