  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.
