  JHKs magnitudes corrected to mean intensity are estimated for LMC type II
Cepheids in the OGLE-III survey. Period-luminosity (PL) relations are derived
in JHKs as well as in a reddening-free VI parameter. Within the uncertainties
the BL Her stars (P < 4 d) and the W Vir stars (P = 4 to 20 d) are co-linear in
these PL relations. 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 uncorrected for any metallicity effects of 18.46 +- 0.10 mag. The type
II Cepheids in the second-parameter globular cluster, NGC 6441, show a PL(VI)
relation of the same slope as that in the LMC and this leads to a cluster
distance modulus of 15.46 +- 0.11 mag, confirming the hypothesis that the RR
Lyrae variables in this cluster are overluminous for their metallicity. It is
suggested that the Galactic variable kappa Pav is a member of the peculiar W
Vir class found by the OGLE-III group in the LMC. Low-resolution spectra of
OGLE-III type II Cepheids with P > 20 d (RV Tau stars) show that a high
proportion have TiO bands; only one has been found showing C_2. The LMC RV Tau
stars, as a group, are not co-linear with the shorter-period type II Cepheids
in the infrared PL relations in marked contrast to such stars in globular
clusters. Other differences between LMC, globular cluster and Galactic field
type II Cepheids are noted in period distribution and infrared colours.
