We review a steady spherical accretion of perfect fluids and show the effects of selfgravitation of the gas. The mass accretion rate is small either when most of the mass of the system is located in the center and in the contrasting case when the mass of the center is small compared to the mass of the accreting fluid. The maximal value of the accretion rate corresponds to the mass of the central black hole being equal 2/3 of the total mass. The main focus is on the stability of selfgravitating flows. While the stability of the accretion in the test fluid case can be proven analytically, the regime of the massive, selfgravitating fluid requires a numerical analysis. Results obtained in the Newtonian approximation show stability against small and large amplitude perturbations.

PACS numbers: 04.40.--b, 97.10.Gz