We discuss the possibility of producing a new kind of nuclear system by putting a few antibaryons inside ordinary nuclei. The structure of such systems is calculated within the relativistic mean-field model assuming that the nucleon and antinucleon potentials are related by the G-parity transformation. The presence of antinucleons leads to decreasing vector potential and increasing scalar potential for the nucleons. As a result, a strongly bound system of high density is formed. Due to the significant reduction of the available phase space the annihilation probability might be strongly suppressed in such systems
