We present results of an extensive search for molecular gas in 14 high
redshift (z > 2) radio galaxies. Radio galaxies with redshifts betwee
n 2.0 and 4.3 were observed during several sessions on two different s
ingle-dish telescopes (LRAM and JCMT) and two interferometric arrays (
VLA and OVRO). No significant CO emission to a 2 sigma limit of a few
times 10(10) K km s(-1) pc(2) was detected in any of these objects. Th
e limits on the CO emission achieved indicate that, assuming a CO-H-2
conversion factor similar to the Galactic value, the mass of enriched
molecular gas in these galaxies is less than 10(11) M.. This suggests
that distant radio galaxies may not be forming stars at the extremely
high rates that have earlier been proposed, although they may still be
forming stars at rates comparable to those of local starburst galaxie
s.