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The cash, estimated to total well over $1 billion a year, flows mostly to the Persian Gulf emirate of Dubai, where many wealthy Afghans now park their families and funds, according to U.S. and Afghan officials. So long as departing cash is declared at the airport here, its transfer is legal.

But at a time when the United States and its allies are spending billions of dollars to prop up the fragile government of President Hamid Karzai, the volume of the outflow has stirred concerns that funds have been diverted from aid. The U.S. Drug Enforcement Administration, for its part, is trying to figure out whether some of the money comes from Afghanistan’s thriving opium trade. And officials in neighboring Pakistan think that at least some of the cash leaving Kabul has been smuggled overland from Pakistan.

“All this money magically appears from nowhere,” said a U.S. official who monitors Afghanistan’s growing role as a hub for cash transfers to Dubai, which has six flights a day to and from Kabul.

Meanwhile, the United States is stepping up efforts to stop money flow in the other direction — into Afghanistan and Pakistan in support of al-Qaeda and the Taliban. Senior Treasury Department officials visited Kabul this month to discuss the cash flows and other issues relating to this country’s infant, often chaotic financial sector.

Tracking Afghan exchanges has long been made difficult by the widespread use of traditional money-moving outfits, known as “hawalas,” which keep few records. The Afghan central bank, supported by U.S. Treasury advisers, is trying to get a grip on them by licensing their operations.

In the meantime, the money continues to flow. Cash declaration forms filed at Kabul International Airport and reviewed by The Washington Post show that Afghan passengers took more than $180 million to Dubai during a two-month period starting in July. If that rate held for the entire year, the amount of cash that left Afghanistan in 2009 would have far exceeded the country’s annual tax and other domestic revenue of about $875 million.

The declaration forms highlight the prominent and often opaque role played by hawalas. Asked to identify the “source of funds” in forms issued by the Afghan central bank, cash couriers frequently put down the name of the same Kabul hawala, an outfit called New Ansari Exchange.

Early last month, Afghan police and intelligence officers raided New Ansari’s office in Kabul’s bazaar district, carting away documents and computers, said Afghan bankers familiar with the operation. U.S. officials declined to comment on what prompted the raid. New Ansari Exchange, which is affiliated with a licensed Afghan bank, closed for a day or so but was soon up and running again.

The total volume of departing cash is almost certainly much higher than the declared amount. A Chinese man, for instance, was arrested recently at the Kabul airport carrying 800,000 undeclared euros (about $1.1 million).

Cash also can be moved easily through a VIP section at the airport, from which Afghan officials generally leave without being searched. American officials said that they have repeatedly raised the issue of special treatment for VIPs at the Kabul airport with the Afghan government but that they have made no headway.

One U.S. official said he had been told by a senior Dubai police officer that an Afghan diplomat flew into the emirate’s airport last year with more than $2 million worth of euros in undeclared cash. The Afghan consul general in Dubai, Haji Rashoudin Mohammadi, said in a telephone interview that he was not aware of any such incident.

The high volume of cash passing through Kabul’s airport first came to light last summer when British company Global Strategies Group, which has an airport security contract, started filing reports on the money transfers at the request of Afghanistan’s National Directorate of Security, the domestic intelligence agency. The country’s notoriously corrupt police force, however, complained about this arrangement, and Global stopped its reporting in September, according to someone familiar with the matter.

Afghan bankers interviewed in Kabul said that much of the money that does get declared belongs to traders who want to buy goods in Dubai but want to avoid the fees, delays and paperwork that result from conventional wire transfers.

The cash flown out of Kabul includes a wide range of foreign currencies. Most is in U.S. dollars, euros and — to the bafflement of officials — Saudi Arabian riyals, a currency not widely used in Afghanistan.

Last month, a well-dressed Afghan man en route to Dubai was found carrying three briefcases stuffed with $3 million in U.S. currency and $2 million in Saudi currency, according to an American official who was present when the notes were counted. A few days later, the same man was back at the Kabul airport, en route to Dubai again, with about $5 million in U.S. and Saudi bank notes.

One theory is that some of the Arab nation’s cash might come from Saudi donations that were supposed to go to mosques and other projects in Afghanistan and Pakistan. But, the American official said, “we don’t really know what is going on.”