Gas accretion of intra cluster gas into the potential well of giant elliptical or cD galaxies can provide the material for both nuclear non-thermal activity and continuous, probably low mass, star formation (Fabian et al. 1982, Valentijn and Bijleveld 1983). In a few dozen cases it has been observed in the nearby universe that the hydrostatic equilibrium of X-ray emitting gaseous atmospheres around cD galaxies is disturbed by the thermal bremsstrahlung cooling in the central high density area, leading to an inflow of gas into the centrally located gE or cD galaxy (“cooling flows”, Jones and Forman 1984). This thermal instability is different from those studied in models of early galaxy formation (Gunn and Gott 1972, Rees and Ostriker 1972) only because of the assumed self-gravitation of the collapsing gas in the galaxy formation scenarios. If however, during early galaxy formation the collapsing gas is accreted by a pre-existing dark potential well, then the processes of early galaxy formation and the observed present epoch cooling flows are likely to be intimately related to each other. The cooling accretion flows could then lead to the original formation of the visible object, and subsequently govern its evolution through the fuelling of star formation and nuclear non-thermal activity.