  We present a study of the properties of the host galaxies of unusual
transient objects of two types, both being sub-luminous compared with the major
classes of supernovae. Those of one type exhibit unusually strong calcium
features, and have been termed 'Ca-rich'. Those of the second type, with
SN2002cx as the prototype and SN2008ha as the most extreme example to date,
have some properties in common with the first, but show typically lower ejecta
velocities, and different early spectra. We confirm important differences in
the environments of the two types, with the Ca-rich transients preferentially
occurring in galaxies dominated by old stellar populations. Quantitatively, the
association of the the Ca-rich transients with regions of ongoing star
formation is well matched to that of type Ia supernovae. The SN2002cx-like
transients are very different, with none of the present sample occurring in an
early-type host, and a statistical association with star-formation regions
similar to that of type II-P supernovae, and therefore a delay time of 30-50
Myrs.
