Abstract: Photoionization of two buckyonions, C$_{60}$@C$_{240}$ and C$_{20}$@C$_{60}$, is investigated by means of time-dependent density-functional theory (TDDFT). The TDDFT-based photoabsorption spectrum of C$_{60}$@C$_{240}$, calculated in a broad photon energy range, resembles the sum of spectra of the two isolated fullerenes, thus illustrating the absence of strong plasmonic coupling between the fullerenes which was proposed earlier. The calculated spectrum of the smaller buckyonion, C$_{20}$@C$_{60}$, differs significantly from the sum of the cross sections of the individual fullerenes because of strong geometrical distortion of the system. The contribution of collective electron excitations arising in individual fullerenes is evaluated by means of plasmon resonance approximation (PRA). An extension of the PRA formalism is presented, which allows for the study of collective electron excitations in multishell fullerenes under photon impact. An advanced analysis of photoionization of buckyonions, performed using modern computational and analytical approaches, provides valuable information on the response of complex molecular systems to the external electromagnetic field.