Verizon Wireless warned customers it may clamp down on heavy users of its wireless data services before an anticipated deluge of Apple Inc iPhone customers.

During the first day of online sales of its new iPhone, the company appeared to be facing heavy demand for the phone on its website, as some customers who tried to buy the iPhone were instead presented with error messages.

Verizon wireless is expected to benefit from strong pent-up demand for the device as AT&T Inc's more than three-year hold on U.S. sales ends.

One perceived advantage of buying the Verizon Wireless iPhone was its offer, at least initially, of unlimited data services for a flat monthly fee of $30. AT&T eliminated its unlimited data plan last year.

But some consumers may be less excited about this if Verizon Wireless starts slowing Web download speeds for the heaviest 5 percent of its smartphone data users, as a document on its website suggests, analysts said.

Neither one is rolling out the red carpet for heavy data users, said Current Analysis analyst Avi Greengart. It makes Verizon Wireless equally unattractive.

Verizon Wireless did not respond to requests for comment on the restriction. The No. 1 U.S. mobile service started taking online orders for its Apple Inc iPhone at 3 a.m. EST on Thursday, a week before it is due to hit store shelves.

SOME WEB ORDER PROBLEMS

Verizon Wireless said sales were mostly running smoothly on the first day of pre-orders, despite problems some customers encountered.

Spokeswoman Brenda Raney said the company was pleased with how the online system performed and that the majority of customers have been able to process their orders with no problems.

But this was not the case for everybody.

We are aware that some customers have received error messages and we are working through the issues with the individuals to ensure they get their order placed, Raney said.

When AT&T and Apple launched pre-orders of the iPhone 4 in June last year, heavy demand caused technical problems on both companies' websites.

Some analysts said Verizon Wireless could sell as many as 13 million iPhones this year. Verizon's earnings guidance for the year assumed sales of 11 million iPhones, as this was in line with the average analyst estimate.

While Verizon Wireless said it would have a limited stock of phones for its first day of sales, Raney said the company was still selling iPhones by mid-afternoon. But the error messages were still showing up for at least some customers.

GOOD BUT WITH TRADE-OFFS

While many of AT&T customers are tied into contracts, analysts still expect some to leave for Verizon due to AT&T's reputation for poor network performance, particularly in cities such as New York and San Francisco.

The first reviews of the new device said the Verizon Wireless iPhone voice service worked better than the AT&T iPhone service. But they noted that switching from AT&T would come with some trade-offs.

Wall Street Journal reviewer Walt Mossberg said that, while the Verizon Wireless iPhone had fewer dropped calls than AT&T's, the Verizon Wireless Web surfing speeds were slower than those on the AT&T iPhone.

New York Times reviewer David Pogue was impressed the Verizon Wireless iPhone made calls in his house, which he described as The Cellphone Signal Torture Chamber of Doom.

But unlike AT&T's iPhone, the Verizon Wireless phone does not allow simultaneous Web surfing and voice calls.

If you receive a call while Web surfing in Verizon's 3G network coverage area, the online session is interrupted so you can answer the phone, but if you are in an area with a slower 2G connection, the call goes directly to voicemail, Pogue said.

The Verizon iPhone may also frustrate some business travelers because it works in far fewer countries than the AT&T iPhone, which supports a more widely used network technology.

Verizon Wireless is a venture of Verizon Communications Inc and Vodafone Group Plc.

AT&T shares closed up 32 cents, or 1 percent, at $27.99 on New York Stock Exchange, where Verizon stock was up 22 cents or 0.6 percent at $36.38.

Verizon also said on Thursday it had authorization to buy back up to 100 million shares of its stock out of the 2.8 billion shares it has outstanding.

(Additional reporting by Jonathan Oatis; editing by Dave Zimmerman, Maureen Bavdek and Andre Grenon)