  We report CO observations towards MS0735.6+7421 a distant cooling core
galaxy, and towards M87, the nearest cooling core in the center of the Virgo
cluster. Both galaxies contain radio cavities that are thought to be
responsible for the heating that can regulate or stop the cooling of the
surrounding gas. In this feedback process, there could still be some gas
cooling along filaments, along the borders of the radio cavities. Molecular gas
is known to exist in clusters with cooling cores, in long and thin filaments
that can be formed behind the rising bubbles inflated by the central AGN. CO
emission was searched for at several locations along the radio lobes of those
two galaxies, but only upper limits were found. These correspond to cold gas
mass limits of a few 10^9 Msol for each pointing in MS0735.6+7421, and a few
10^6 Msol in M87. This non detection means that either the cooling is strongly
reduced by the AGN feedback or that the gas is cooling in very localized places
like thin filaments, possibly diluted in the large beam for MS0735.6+7421. For
M87, the AGN heating appears to have stopped the cooling completely.
