WITH the old red stone ramparts of a Portuguese fort rising in the background, an Indian family gathered tentatively at the edge of the Arabian Sea. Intrigued by the novelty of ocean waves, two young girls skipped back and forth, until a rogue wave finally caught them and soaked the hems of their saris.

Goa, a stop on the hippie trail in the 1960's, then a winter destination for discount charter jets filled with Europeans, still attracts about 10 percent of the 2.5 million people who visit India annually. But now, in a new twist for a land long associated with sin and sand, this Rhode Island-size state on India's southwest coast is becoming a well-behaved family destination, attracting India's expanding middle class.

Since 2000, the number of foreign visitors to Goa has dropped by 7 percent, to 272,000, while the number of "domestic" visitors has jumped by 36 percent, to 1.3 million.

"With all the publicity they made in India, Goa is attracting a new class of people," Herman Kuhne, a Swiss resident, said on a recent night at Britto's Restaurant on Baga Beach, where he was the lone European, surrounded by about 20 tables of Indian families. "Last December, this road was totally blocked with cars from other states."

Cajie Britto, owner of this seafood landmark, said that after the European charter jets stop coming in mid-April, Goa's hotels fill with Indians on summer school holidays.

With many shops, inns and restaurants closing in the off season, Goans may still harbor the stereotype that European tourists spend more than Indians.

"The tourism industry is slow to realize that the future of tourism in Goa is Indian," said Claude Alvares, an environmentalist here. "The British fellow counts his paise and argues over a 10-rupee bottle of water. The Indians come down from Bombay. They don't look at the price sheets. They just say they want this or that." Antonio Sousa, chancellor of the Portuguese consulate, said of the deeply discounted European charters: "For a taxi driver in Stockholm, it's cheaper to come down here in January than to keep the heat on at home."

The season of Northern Europe's sunburned-pink tribe, largely British, runs from May through October. While Europeans account for two-thirds of foreign visitors, North Americans account for only 4 percent, or about 10,000 a year.

The off season provides a more Indian experience. The same beaches that were covered in January with nearly naked Europeans are covered in May with decorously attired Indians, often in saris, shirts or long pants. On a recent Sunday afternoon in Old Goa, at the 16th-century Basilica of Bom Jesus, clouds of Hindu women in saris floated among the twisted Bernini columns, sometimes pausing to pray before the gilded nave or before the 450-year-old remains of St. Francis Xavier, encased in a glass tomb.

This year, the Hyatt and the Radisson have opened hotels in Goa, joining InterContinental and Marriott. With 2,000 hotels, inns and bed-and-breakfasts offering 33,000 rooms in India's smallest state, Indian tourists will be the key for Goa's reaching its goal of 50 percent expansion of tourism by 2006, N. Suryanarayana, state tourism director, said in an interview.

Goa is getting some of the world's newest tourists. Last year saw the first groups from China and 10,000 Russians on charter flights from Moscow.

But in the last two years, foreign arrivals have been cut by 10 percent and air charter by one-third by European fears of terrorism, although no terrorist attacks have been recorded in this state, where the population is largely Hindu or Catholic. Just as some Europeans decided to stay home, some Indians decided to travel domestically.

"Indians who used to travel to Britain and Europe have also stopped traveling overseas," said Atul Lall, manager of Fort Aguada Beach Resort, part of the Taj chain. Year round, Indians now account for 60 percent of guests at this five-star resort, up from 40 percent five years ago, he said. "Our Indian numbers have picked up quite a bit, compensating for the drop in foreigners."

Indians' discovery of Goa is also a function of the mathematics of a growing middle class. Only 20 percent of Indians may be able to afford a vacation in Goa. But 20 percent of one billion people is 200 million. In late May, New Delhi travel agencies were offering three-night hotel and air packages to Goa for as little as $360 a person.

Transportation plays a role. Naturally isolated by mountains to the south and the east, bowl-shaped Goa and its 60 miles of smooth beaches survived as a little-known Portuguese enclave for 451 years. After India "liberated" Goa from Portuguese colonial rule in 1961, Indians were slow to discover Goa. Access from Bombay, the nearest major city, took about 14 hours, whether by road, rail or boat. But five years ago, the Konkan Railway came through here from Bombay, about 375 miles to the north. Using this new, largely coastal route, rail travel time was cut to eight hours. In a new step, "Superexpress" service is to start this month, cutting train travel time to four and a half hours.

With the new domestic connections, more and more affluent Indians are planning to retire in Goa, which was ranked in mid-May by India Today magazine as "India's best state" for several indicators, including health care.