A sensitive search for millimeterwave CO emission in 8 damped Lyman-al
pha systems, 3 heavy element absorption line systems and one emission
line galaxy, at redshifts ranging from 0.5 to 2.8, have yielded upper
limits to the amount of molecular gas. The limits still allow relative
ly high H-2 masses, but our results show that damped Lyman-alpha syste
ms are not similar to the hyperluminous infrared galaxies at high reds
hifts found in the IRAS database. One tentative detection of CO emissi
on at z(a) = 2.47 remains, but is very uncertain. We are not able to c
onfirm a claimed detection of CO emission at z(a) = 2.14 towards Q0528
-250.