  We have estimated JHKs magnitudes corrected to mean intensity for LMC type II
Cepheids found in the OGLE-III survey. Period-luminosity relations (PLRs) are
derived in JHKs as well as in a reddening-free VI parameter. The BL Her stars
(P<4d) and the W Vir stars (P=4 to 20d) are co-linear in these PLRs. The slopes
of the infrared relations agree with those found previously for type II
Cepheids in globular clusters within the uncertainties. Using the pulsation
parallaxes of V553 Cen and SW Tau, the data lead to an LMC modulus of
18.46+-0.10 mag, uncorrected for any metallicity effects. We have now
established the PLR of type II Cepheids as a distance indicator by confirming
that (almost) the same PLR satisfies the distributions in the PL diagram of
type II Cepheids in (at least) two different systems, i.e. the LMC and Galactic
globular clusters, and by calibrating the zero point of the PLR. RV Tau stars
in the LMC, as a group, are not co-linear with the shorter-period type II
Cepheids in the infrared PLRs in marked contrast to such stars in globular
clusters. We note differences in period distribution and infrared colors for RV
Tau stars in the LMC, globular clusters and Galactic field. We also compare the
PLR of type II Cepheids with that of classical Cepheids.
