  We have obtained sensitive upper limits on the CO J=2-1 and CO J=3-2 emission
lines for five faint blue galaxies with redshifts $z\sim 0.5$ using the IRAM
30~m telescope. These observations would have been able to detect the luminous
infrared galaxy IRAS F10214+4724 if it were located at this redshift and
unlensed. However, they are not sensitive enough to detect the prototype
starburst galaxy M82 or the HII galaxy UM448 if they were located at this
redshift. Our upper limits for the CO emission are consistent with between 19%
and 66% of the total galactic mass being in the form of molecular hydrogen, and
thus shed little light on the ultimate fate of these galaxies.
