More than a quarter of iPhones sold in the US are being used on a network other than that of Apple's exclusive partner, AT&T, leading to significantly reduced revenues for Apple.

Research by analysts suggests that about a million iPhones - 27 per cent of the total sold - have been unlocked, allowing them to run on unauthorised networks. As a result, Apple is missing out on the share of monthly fees it would get if the phones were run on AT&T's network.

The figure is significantly higher than the previous estimate of 750,000, and could contribute to as much as $500 million in lost revenue, making it a "significant strategic dilemma for Apple," Toni Sacconaghi, an analyst at Bernstein Research, wrote.

Apple has said that the number of unlocked iPhones was "significant" but has declined to give details.

The iPhone, which was launched last summer, is tied to a single network in each country, with carriers agreeing to share a portion of customers' monthly tariff with Apple in return for being the sole distributor of the device.

Mr Sacconaghi based his analysis on figures from Apple which suggested that the company sold 3.75 million iPhones last year. Subtracting the 2 million devices that AT&T said it had 'activated', and an estimated 315,000 sold in Europe so far, that left 1.45 million phones 'missing in action', Mr Sacconaghi said.

Assuming 480,000 of those were being held by AT&T as inventory, that left about a million that had been 'unlocked', meaning that their owners had downloaded a piece of software which allows the phone to operate on whichever network they choose.

The figure was astounding, Mr Sacconaghi said, given that an unlocked iPhone generates about 50 per cent less revenue and about 75 per cent less profit than one running on an authorised network. If 30 per cent of the 10 million iPhones Apple hoped to sell this year were unlocked, then the company's earnings may be about 37 cents per share lower in each of the next two years, he said.

Apple has declined to comment on the report.

Another analyst firm, Piper Jaffray & Co., estimates that just under 850,000 iPhones - or 25 percent of the total sold - were unlocked last year.

Apple shares closed unchanged at $130.01 yesterday. The stock has fallen by more than 25 per cent in the past two weeks amid concerns that a slowdown in consumer spending may affect sales of electronic goods like computers and media players.

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