Until now the U.S. market has mainly been a local consumer market. But that could change, adding to strong domestic demand. The government is relaxing visa requirements for Chinese visitors, hoping to attract the large number of tourists who head to Europe to snap up luxury goods.

"The stronger economy and loosening of visa restrictions for the Chinese mean that business this year will benefit from both affluent locals and tourism," said Milton Pedraza, CEO of the Luxury Institute, a U.S. consulting firm.

To welcome the expected boost in tourists, luxury houses are making sure their flagship stores are in tiptop shape. Burberry Group (BBRYF) recently renovated its main Chicago boutique. Hermès plans to refurbish and expand its Rodeo Drive store in Beverly Hills, Calif. Next year, the company is scheduled to move its current store in Miami -- a gateway for Latin American visitors -- to a larger location in the city's up-and-coming Design District.

"We didn't open any new stores or do any renovations in 2012 in the U.S., so (growth) was really done through the existing store network," said Axel Dumas, Hermès' chief operating officer. Dumas is set to become joint-CEO alongside Thomas later this year.

At Hermès, sales in the Americas last year rose 14% to $753 million, while sales in Asia excluding Japan increased 25% to $1.4 billion. The company doesn't break out U.S. figures. Total sales were $4.6 billion for the year.

Though executives are enthusiastic about the U.S. growth, they are also realistic about its limits. As recently as 2007, luxury brands were opening dozens of stores in smaller cities from Seattle to Nashville, Tenn. But analysts say luxury-goods sales haven't lived up to expectations in some of those places.

"Where some have gone too far is in thinking Middle America is going to be buying luxury," says HSBC's Belge.

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