  X-ray Flashes (XRFs) are, like Gamma-Ray Bursts (GRBs), thought to signal the
collapse of massive stars in distant galaxies. Many models posit that the
isotropic equivalent energies of XRFs are lower than those for GRBs, such that
they are visible from a reduced range of distances when compared with GRBs.
Here we present the results of two epoch Hubble Space Telescope imaging of two
XRFs. These images taken approximately 45 and 200 days post burst reveal no
evidence for an associated supernova in either case. Supernovae such as SN
1998bw would have been visible out to z ~1.5 in each case, while fainter
supernovae such as SN 2002ap would have been visible to z ~ 1. If the XRFs lie
at such large distances, their energies would not fit the observed correlation
between the GRB peak energy and isotropic energy release, in which soft bursts
are less energetic. We conclude that, should these XRFs reside at low redshifts
($z<0.6$), either their line of sight is heavily extinguished, or they are
associated with extremely faint supernovae, or, unlike GRBs, these XRFs do not
have temporally coincident supernovae.
