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(abridged) Type II and anomalous Cepheids (ACs) are useful distanceindicators when there are too few classical Cepheids or when RR Lyrae stars aretoo faint. We study the sample of 335 Type II and ACs in the Small and LargeMCls detected in OGLE-III data.The SEDs are constructed and fitted with a dustradiative transfer model, thereby leading to a determination of luminosity andeffective temperature.In addition, a subsample of targets is investigated forpossible binarity by looking for the light-time travel effect (LITE).Hertzsprung-Russell diagrams (HRD) are constructed and compared to evolutionarytracks and theoretical instability strips (ISs). In agreement with previoussuggestions, 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 explainedby the evolution of $\sim$1.1-2.3~\msol\ stars. The evolution of the W Virsubclass is not clear. A relation to binarity might be at the origin of the WVir stars, which has already been explicitly suggested for the peculiar W Virstars. For $\sim60\%$ of the RV Tau and $\sim 10\%$ of the W Vir objects aninfrared excess is detected from the SED fitting. A recent result is confirmedthat stars exist with luminosities below that predicted from single-starevolution, which show a clear infrared excess, and the shape of the excesssuggests a connection to binary evolution. The investigation of the LITE effectrevealed 20 systems that appear to show periodic variations and may be newbinaries, although this study requires follow-up. About 40 stars showsignificant period changes.

Luminosities and infrared excess in Type II and anomalous Cepheids in the Large and Small Magellanic Clouds