We have developed a method for selecting the most luminous galaxies detecte
d by IRAS based on their extreme values of R, the ratio of 60 mu m and B-ba
nd luminosity. These objects have optical counterparts that are close to or
below the limits of Schmidt surveys. We have tested our method on a 1079 d
eg(2) region of sky, where we have selected a sample of IRAS sources with 6
0 mu m flux densities greater than 0.2Jy, corresponding to a redshift limit
z similar to 1 for objects with far-IR luminosities of 10(13) L.. Optical
identifications for these were obtained from the UK Schmidt Telescope plate
s, using the likelihood ratio method. Optical spectroscopy has been carried
out to reliably identify and measure the redshifts of six objects with ver
y faint optical counterparts, which are the only objects with R > 100 in th
e sample. One object is a hyperluminous infrared galaxy (HyLIG) at z = 0.83
4. Of the remaining, fainter objects, five are ultraluminous infrared galax
ies (ULIGs) with a mean redshift of 0.45, higher than the highest known red
shift of any non-hyperluminous ULIG prior to this study. High excitation li
nes reveal the presence of an active nucleus in the HyLIG, just as in the o
ther known infrared-selected HyLIGs. In contrast, no high excitation lines
are found in the non-hyperluminous ULIGs. We discuss the implications of ou
r results for the number density of HyLIGs at z < 1 and for the evolution o
f the infrared galaxy population out to this redshift, and show that substa
ntial evolution is indicated. Our selection method is robust against the pr
esence of gravitational lensing if the optical and infrared magnification f
actors are similar, and we suggest a way of using it to select candidate gr
avitationally lensed infrared galaxies.