For seven faint southern Cepheids (WW Car, SX Car, UZ Car, UY Car, GX Car, HW Car, YZ Car), we have determined their atmospheric parameters and chemical composition for the first time based on ten high-resolution (R=50000) spectra taken with the 1.5-m Hexapod telescope at the Joint Observatory of the Northern Catholic University (Antofagasta, Chile) and the Ruhr University (Bochum, Germany). Six objects from the list demonstrate atmospheric parameters and chemical composition typical of Cepheids that have passed through the first dredge-up phase, while WW Car is probably an anomalous Cepheid. According to our preliminary estimates, it has an overabundance of CNO, a deficit of sodium and aluminium, and a slight deficit of magnesium, with iron and other elements being underabundant relative to the Sun.