  (abridged) Type II and anomalous Cepheids (ACs) are useful distance
indicators when there are too few classical Cepheids or when RR Lyrae stars are
too faint. We study the sample of 335 Type II and ACs in the Small and Large
MCls detected in OGLE-III data.The SEDs are constructed and fitted with a dust
radiative transfer model, thereby leading to a determination of luminosity and
effective temperature.In addition, a subsample of targets is investigated for
possible binarity by looking for the light-time travel effect (LITE).
Hertzsprung-Russell diagrams (HRD) are constructed and compared to evolutionary
tracks and theoretical instability strips (ISs). In agreement with previous
suggestions, the BL Her subclass can be explained by the evolution of
$\sim$0.5-0.6~\msol\ stars evolving off the ZAHB and the ACs can be explained
by the evolution of $\sim$1.1-2.3~\msol\ stars. The evolution of the W Vir
subclass is not clear. A relation to binarity might be at the origin of the W
Vir stars, which has already been explicitly suggested for the peculiar W Vir
stars. For $\sim60\%$ of the RV Tau and $\sim 10\%$ of the W Vir objects an
infrared excess is detected from the SED fitting. A recent result is confirmed
that stars exist with luminosities below that predicted from single-star
evolution, which show a clear infrared excess, and the shape of the excess
suggests a connection to binary evolution. The investigation of the LITE effect
revealed 20 systems that appear to show periodic variations and may be new
binaries, although this study requires follow-up. About 40 stars show
significant period changes.
