The photoionization of a two-shell (“onion”) endohedral A@C_N1@C_N2 is considered. The effect of the fullerenes shells upon photoelectron from atom A is taken into account substituting the action of the fullerene by two zero-thickness “bubble potentials”. The fullerenes shells polarization is included assuming that the radius of the outer shell R₂ is much bigger than the inner R₁ and both much exceed the atomic radius r.

The interaction between shells C_N1 and C_N2 is taken into account in the Random Phase Approximation (RPA). The effect of photoelectron scattering by both “bubble potentials” is included in the RPA frame.

         We present results for photoionization cross sections, dipole and non-dipole angular anisotropy parameters for outer in Ar and outer and intermediate in Xe subshells for endohedrals with two-shell fullerenes Ar@C₆₀@C₂₄₀ and Xe@C₆₀@C₂₄₀ and compare it to the respective data for isolated atoms. We have investigated effects of photoelectron scattering by two zero-thickness potential wells and modification of the incoming photon beam due to dipole polarization of both fullerenes shell. It is possible to have in such a system strong interference features that are similar to a sort of standing waves between the two fullerenes shell.

         A whole variety of resonances are found that obviously are far from being a simple sum of effects, given by single fullerenes shells. Particularly sensitive to the surrounding of fullerenes shell are non-dipole angular anisotropy parameters. For them, however, the effect of deviation of real fullerenes shell potential from the ideal spherical shape could be of importance.

         We admit that the moment when investigation of photoionization of such objects as A@C₆₀@C₂₄₀ or similar will take place is not literally tomorrow. However, we hope to see them being performed in not too distant future. We believe that possible findings will justify the efforts.