[en] Hot intracluster gas associated with clusters of galaxies can cool and accrete into stationary or slowly moving giant galaxies near the cluster center. Enhanced soft X-ray emission and faint extranucler optical emission lines observed in M87 (in the Virgo cluster) and NGC 1275 (in the Perseus cluster) strongly suggest that this process is occurring. In both cases, however, the flow appears to be thermally unstable and the central accretion is in the form of clouds. Small variations in the initial magnetic field strength may initiate the thermal instability. Such instabilities are required in M87 and NGC 1275 since it is otherwise difficult to account for the observation of cool (Tapprox. =10⁴ K) gas far from the nucleus.We calculate models for steady accretion flow produced by optically thin radiative losses. These flows serve as a basis for an instability analysis and provide an upper limit to the mass accretion rate. Application of these models to M87 suggests that the accretion rate in the case is < or approx. =30M/sub sun/yr^-1. The accretion rate would be less than this upper limit if thermal instabilities were well developed in the soft X-ray emitting regions. However, it is likely that much of this gas will never reach the nucleus since nonthermal energy is released in the nucleus at a rate comparable to the pwer generated in the accretion flow (10⁴⁹--10⁵⁰ergs yr^-1).We also outline a possible explanation of the small unresolved X-ray source in M87 in terms of the interaction of infalling accretion clouds with the larg e nuclear gas cloud