Cepheids, the principal distance indicators, point to the existence of two inner Galactic spiral arms in the immediate solar neighborhood (within 5 kpc). However, the available Cepheids are clearly insufficient for a detailed study of the structure of these arms. Fortunately, southern-sky monitoring (the ASAS project) has led to the discovery of many new variable stars, more than one thousand of which have been identified as possible Cepheids. To improve the classification and to construct reliable light curves for new Cepheids, we have begun their regular photometric observations. Here, we present the first results: 1192 photoelectricBV Ic observations were performed for 33 classical Cepheidswith the 76-cm telescope of the South-African Astronomical Observatory (SAAO, the South-African Republic) from December 2006 to January 2008. We provide tables of observations and V light and B-V and V-Ic color curves. The new observations together with ASAS-3 data have been used to improve the elements of the light variations.