  We discuss the influence of a single or double fullerenes shell upon
photoionization and vacancy decay of an atom, stuffed inside the fullerenes
construction. The main manifestations of this influence are additional
structures in the photoionization cross-section and variation of the vacancy
decay probability. The main mechanisms, with which fullerenes shells affect the
processes in caged atoms is the scattering of the outgoing electrons by the
fullerenes shell and modification of the photon beam due to fullerenes shell
polarization. General consideration will be illustrated by numeric calculations
where C60 and C240 will be chosen as fullerenes and Ar and Xe as caged atoms.
