The International Amateur Athletic Federation decided at a meeting of its council to put the cases to arbitration and let the athletes compete in Atlanta. The arbitration panel is normally not able to sit for at least three months.
If the IAAF arbitration panel decides the athletes should be banned, their results at the Olympics will be annulled.
Capobianco tested positive for the steroid stanozolol at a meeting in the Dutch town of Hengelo last May but an Australian athletics appeals tribunal ruled against a compulsory four-year ban, saying there were serious flaws in testing procedures.
Bevilacqua, one of the top six jumpers in the world this year, was caught twice with the banned stimulant ephedrine in her body in May. But an Italian panel decided she had taken the drug by mistake.