The electronic phase separation in doped antiferromagnetic semiconductors and materials exhibiting colossal magnetoresistance, with the charge-carrier density n close to the density at which the entire crystal becomes ferromagnetic, is investigated theoretically. The case of wide s bands and that of double exchange are investigated. At a first-order phase transition from the phase-separated state to the ferromagnetic state should take place on increase of the temperature. At a re-entrant phase separation is possible when, with increasing temperature, first, the first-order phase transition from the ferromagnetic state to the phase-separated state takes place and, then, the latter melts.