  We discuss the X-ray properties of the cooling flows in a sample of thirty
highly X-ray luminous clusters of galaxies observed with the ASCA and ROSAT
satellites. We demonstrate the need for multiphase models to consistently
explain the spectral and imaging X-ray data for the clusters. The mass
deposition rates of the cooling flows, independently determined from the ASCA
spectra and ROSAT images, exhibit good agreement and exceed 1000 solar masses
per year in the largest systems. We confirm the presence of intrinsic X-ray
absorption in the clusters using a variety of spectral models. The measured
equivalent hydrogen column densities of absorbing material are sensitive to the
spectral models used in the analysis, varying from average values of a few
10^{20} atom/cm^2 for a simple isothermal emission model, to a few 10^{21}
atom/cm^2 using our preferred cooling flow models, assuming in each case that
the absorber lies in a uniform foreground screen. The true intrinsic column
densities are likely to be even higher if the absorbing medium is distributed
throughout the clusters. We summarize the constraints on the nature of the
X-ray absorber from observations in other wavebands. A significant part of the
X-ray absorption may be due to dust.
