  We have undertaken a search for millimetre-wave band absorption (through the
CO and HCO+ rotational transitions) in the host galaxies of reddened radio
sources (z = 0.405-1.802). Despite the colour selection (optical-near infrared
colours of V - K > 5 in all but one source), no absorption was found in any of
the eight quasars for which the background continuum flux was detected. On the
basis of the previous (mostly intervening) H2 and OH detections, the limits
reached here and in some previous surveys should be deep enough to detect
molecular absorption according to their V - K colours. However, our survey
makes the assumption that the reddening is associated with dust close to the
emission redshift of the quasar and that the narrow millimetre component of
this emission is intercepted by the compact molecular cores. By using the known
millimetre absorbers to define the colour depth and comparing this with the
ultra-violet luminosities of the sources, we find that, even if these
assumptions are valid, only twelve of the forty objects (mainly from this work)
are potentially detectable. This is assuming an excitation temperature of 10 K
at z=0, with the number decreasing with increasing temperatures (to zero
detectable at 100 K).
