The NATO force in Bosnia, which had 60,000 men at its disposal at the beginning of its mandate, failed in nine years to arrest the two men, who were indicted by the International Criminal Tribunal in The Hague in 1995 for war crimes and crimes against humanity.
The 7,000-man European force that succeeded NATO last December has had no greater success until now in tracking them down, despite a five-million-dollar (4.3-million-euro) price on their heads.
Many are amazed that NATO, with its intelligence capabilities and unassailable military superiority, was unable to capture Karadzic, 59, and Mladic, 62.
Experts familiar with the background told AFP that it would have been possible to arrest the two in the early stages, but the political will to do so was lacking.
"Every day we received information about Karadzic. We filmed his movements. It was easy to arrest him. But we never got the green light to act," said a former official of a European country's secret services who was in Bosnia when the two men went on the run.
"Conversely, if we had launched an operation against Mladic, who hid for a long period in caves, protected by some 500 soldiers, we would have had casualties on our side," he said.
NATO-member France, which was committed heavily to the NATO Stabilisation Force in Bosnia, was suspected by the United States of not doing enough to track the two down.
But even though Washington put up the reward for information leading to the arrest of people wanted for crimes committed during the breakup of the former Yugoslavia, it did not seem to be intent on arresting them either.
"When we could have captured Karadzic, SFOR's commander-in-chief, the American Admiral Leighton Smith, stopped us, saying that he did not have orders from Washington to arrest him," the former agent said.
"No doubt the United States did not want to risk casualties in Bosnia."
But then US interest picked up again in mid-2003, amid a failure to nab ousted Iraqi leader Saddam Hussein, or Al-Qaeda leader Osama bin Laden, a source involved with the security services in Paris said.
"The CIA (Central Intelligence Agency) then offered several million dollars to a former European military official to tap his networks among Bosnian Serbs to find Karadzic and Mladic," he added, saying this proved how little effort Washington had put into the hunt in the meantime.
Specialists also point to the inadequate coordination between the secret services of the different SFOR member countries.
Other factors contributed to the two indictees' escape: support from Bosnian Serbs, including certain leaders, the availability of funds, help from elements of the army in Belgrade for Mladic and extreme caution by the two fugitives in communicating.
"They stopped using mobile or satellite phones a long time ago," an officer involved in the search operations said.
"Even by intercepting the underground optical fibre network of the former Yugoslav army we did not learn a lot," he said.
According to persistent but non-verifiable rumors, Karadzic has benefited from the hospitality of Serbian Orthodox monasteries in Bosnia and in Serbia.
Mladic has been helped for many years by his old companions-in-arms in the former Yugoslav army.
An official of the Serbia-Montenegro secret services acknowledged in June that Mladic had lived in Belgrade until 2002, either at home or in military buildings, but that he had later disappeared.
Belgrade had denied until that time it had any knowledge of Mladic's wherabouts.