  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.
