  We present a catalogue of 179 hyperluminous infrared galaxies (HLIRGs) from
the Imperial IRAS-FSS Redshift (IIFSCz) Catalogue. Of the 92 with detections in
at least two far infrared bands, 62 are dominated by an M82-like starburst, 22
by an Arp220-like starburst and 8 by an AGN dust torus. On the basis of
previous gravitational lensing studies and an examination of HST archive images
for a further 5 objects, we estimate the fraction of HLIRGs that are
significantly lensed to be 10-30%. We show simple infrared template fits to the
SEDs of 23 HLIRGs with spectroscopic redshifts and at least 5 photometric
bands. Most can be fitted with a combination of two simple templates: an AGN
dust torus and an M82-like starburst. In the optical, 17 of the objects are
fitted with QSO templates, 6 are fitted with galaxy templates. 20 of the 23
objects (87%) show evidence of an AGN either from the optical continuum or from
the signature of an AGN dust torus, but the starburst component is the dominant
contribution to bolometric luminosity in 14 out of 23 objects (61%). The
implied star-formation rates, even after correcting for lensing magnification,
are in excess of 1000 Mo /yr. We use infrared template-fitting models to
predict fluxes for all HLIRGs at submillimetre wavelengths, and show
predictions at 350 and 850 mu. Most would have 850 mu fluxes brighter than 5
mJy so should be easily detectable with current submillimetre telescopes. At
least 15% should be detectable in the Planck all-sky survey at 350 mu and all
Planck all-sky survey sources with z < 0.9 should be IIFSCz sources. From the
luminosity-volume test we find that HLIRGs show strong evolution. A simple
exponential luminosity evolution applied to all HLIRGs would be consistent with
the luminosity functions found in redshift bins 0.3-0.5, 0.5-1 and 1-2.
