In the second part of the OGLE-III Catalog of Variable Stars (OIII-CVS) we present 197 type II Cepheids and 83 anomalous Cepheids in the Large Magellanic Cloud (LMC). The sample of type II Cepheids consists of 64 BL Her stars, 96 W Vir stars and 37 RV Tau stars. Anomalous Cepheids are divided into 62 fundamental-mode and 21 first-overtone pulsators. These are the largest samples of such types of variable stars detected anywhere outside the Galaxy. We present the period-luminosity and color-magnitude diagrams of stars in the sample. If the boundary period between BL Her and W Vir stars is adopted at 4 days, both groups differ significantly in (V-I) colors. We identify a group of 16 peculiar W Vir stars with different appearance of the light curves, brighter and bluer than ordinary stars of that type. Four of these peculiar W Vir stars show additional eclipsing modulation superimposed on the pulsation light curves. Four other stars of that type show long-period secondary variations which may be ellipsoidal modulations. It suggests that peculiar W Vir subgroup may be related to binarity. In total, we identified seven type II Cepheids simultaneously exhibiting eclipsing variations which is a very large fraction compared to classical Cepheids in the LMC. We discuss diagrams showing Fourier parameters of the light curve decomposition against periods. Three sharp features interpreted as an effect of resonances between radial modes are detectable in these diagrams for type II Cepheids.
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