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We present 1256 new photometric observations of 36 Cepheids with periods longer than 8 days. The majority are likely type II Cepheids, but we have included about a dozen classical Cepheids for comparison purposes, a few stars of uncertain type, and one putative RV Tauri star. We discuss the appearance of the light curves, the Fourier parameters, and the light-curve stability in terms of differentiation between type I and type II Cepheids. Although we encounter the same difficulties as previous investigators in using these parameters for this purpose, we are able to identify some stars of particular interest, including several likely type I Cepheids at large distances from the Galactic plane. Six stars with especially large period changes are identified and discussed.