  We present preliminary results of a follow-up survey which aims to
characterise in detail those galaxies which hosted Type Ia supernovae found by
the Supernova Cosmology Project (SCP). Our survey has two components: Hubble
Space Telescope imaging with STIS and Keck spectroscopy with ESI, the goal
being to classify each host galaxy into one of three broad
morphological/spectral classes and hence to investigate the dependence of
supernovae properties on host galaxy type over a large range in redshift. Of
particular interest is the supernova Hubble diagram characterised by host
galaxy class which suggests that most of the scatter arises from those
occurring in late-type irregulars. Supernovae hosted by (presumed dust-free)
E/S0 galaxies closely follow the adopted SCP cosmological model. Although
larger datasets are required, we cannot yet find any significant difference in
the light curves of distant supernovae hosted in different galaxy types.
