[en] Positron-containing negative ions are examined by the method of the Fock self-consistent field in a single-configuration approximation and possibilities of the existence of such systems in a ground state are defined. An algorithm and a program of numerical solution of the Hartree-Fock equations have been developed for solving this problem. e⁺A^- systems with the nucleus charge from 1 to 17 are considered. In all the cases the affinity of negative ions with positrons is shown to be positive, which confirms the possibility of the existence of such exotic formations relative to a decay into a negative ion and a positron. However, these systems turned out to be energy-unstable relative to their decay to produce the corresponding neutral ion and positronium. The experimental and theoretical works on positron-containing systems available are reviewed