Home prices have risen in the Hamptons and in the more modest towns along Suffolk County’s South Shore, but elsewhere on Long Island prices are down or relatively flat, according to a pair of new reports.

In the Hamptons the median home price was $780,000 in the first quarter, nearly 12 percent more than in the same period a year earlier, according to a report on East End home prices scheduled to be released Thursday by Prudential Douglas Elliman Real Estate and the appraisal firm Miller Samuel.

On Long Island as a whole, not including the East End, the median price of $350,000 was unchanged in the first quarter compared to the same period in 2011, according to a companion report. Aside from the Hamptons, the only area with significant price gains was Suffolk County’s South Shore, where the median price — the midpoint in a series — was up 11.5 percent, to $269,000, compared to the same period in 2011.

It’s no accident that the biggest price gains were in the highest- and lowest-priced regions, said Jonathan Miller, president of Miller Samuel.

“On the one hand, you have the high end of the market that is seeing strength, and that’s Wall Street, foreign buyers, wealthy individuals,” Miller said. “The upper end of the market continues to fare better than the rest of the market.”

At the same time, he said, rock-bottom mortgage interest rates are drawing first-time home buyers and other bargain seekers to less expensive homes.

“You put them together and you have this strength at the low and the high ends and not much change in the middle,” he said.

Buyers are having a hard time qualifying for mortgages, since credit standards have tightened in the wake of the housing crash, said Dottie Herman, president of Prudential Douglas Elliman.

“The market on Long Island in general is holding its own, but it’s still fragile,” she said. “It’s all going to depend on the financing.”

An expected wave of foreclosures this year could pull prices down, though probably not by much, Miller said.

Even within the Hamptons, more buyers are gravitating to the low and high ends of the market, said Judi Desiderio, president of Town & Country Real Estate in East Hampton.

Comparing the first quarters of 2011 and 2012, the sharpest increases in sales were for homes under $500,000, and those from $3.5 million to $5 million, she said. Town & Country produces its own research, using data from the Long Island Real Estate Report. The reports by Elliman and Miller Samuel draw on data from the same source, as well as the Multiple Listing Service of Long Island.

Buyers say they don’t want to miss the bottom of the market, Desiderio said.

“We knew that the low end was very active,” she said. “But the significance here is that the guys who are spending $3.5 million to $5 million on second homes are very comfortable jumping in right now.”