The present state of the problem of quasinuclear systems containing antibaryons ($B\bar B$ and $2N2\bar N$ mesons and $2N\bar N$ baryons) is reviewed. A discussion is presented of the experimental data (the resonances which are strongly coupled with the $N\bar N$ channel, with masses of about 2 GeV) and of the central theoretical questions (the energy spectra and properties of the quasinuclear systems, the annihilation widths and shifts of the quasinuclear levels, the $p\bar p$ atom, and radiative transitions from atomic states to quasinuclear states).