Sheik Nayaf Khreishe, the leader of a noble Bedouin clan, owns an elegant stone house with a solar powered telephone and rides through his ancestral desert in a baby-blue air-conditioned Buick.

But in the afternoon, when warm breezes blow off the sand and his followers troop in to have their problems settled, they find the sheik sitting cross-legged under a goat-hair tent like the one he was born in half a century ago.

He put up the tent right in his front yard, just below the solar panels, as the appropriate place to receive supplicants and offer them bitter coffee and sweet tea. When he sits there on a cushion, dispensing wisdom according to traditions reaching back before Mohammed, it seems also to be a quiet affirmation of Bedouin pride and a measure of how much the sheik cherishes a culture that he knows to be on the road to oblivion.

For Jordan's Bedouins, one of the largest groups of desert wanderers whose folkways have played a decisive role in shaping Arab culture throughout the Middle East, are losing their battle with the 20th century.

Their cousins in other Arab countries -- Saudi Arabia, Egypt, Syria -- also are gradually abandoning their nomadic desert life in favor of cities and settlements. But the process in Jordan has been hastened by an unusual five-year drought that has drained the desert of its camel and sheep herds and has accelerated the move toward sedentary life that experts here conclude was inevitable anyway.

"There is no doubt; the Bedouins are on their way out," said Lt. Atif Abdul Karim Qadi, a Bedouin born in a goat-hair tent in the northern desert of Jordan and who serves in the celebrated Jordanian Desert Patrol, or Camel Corps.

In the 1950s, Jordanian government experts estimated as many as 220,000 Bedouins lived in goat-hair tents, or "hair houses" as they are called in Arabic, and wandered with their herds of goats, sheep and camels across the three-fourths of Jordan's surface that is desert.

By the time a census was taken in 1961, the number had dropped to about 95,000. Now, according to a careful field study by a group of researchers from the University of Jordan, there are fewer than 60,000 Bedouins who still live a semblance of the life of their forefathers.

Their numbers have been shrinking even more rapidly during the last five years because of the drought. "Within 10 years, there won't be any more nomadic Bedouins out there," predicted Lt. Col. Anbar Dahash, director of the Desert Patrol and an urbanized Bedouin. "The Bedouins are leaving the grazing lands and coming to live in the cities."

The result is a gradual withering away of a romantic lifestyle that has caught the imagination of the West since the days of the first European desert explorers and through the writings of Lawrence of Arabia.

The image of the camel swaying across a wasteland carrying a robed Bedouin is being replaced by a pickup truck bouncing along a desert road bringing drinking water to a collection of cement or clay huts where the Bedouins have gathered in order to send their children to school and use the health clinic.

"Whether we like it or not, and whether the Bedouins like it or not, the camel is being overtaken by the Land Rover and the airplane," concluded the University of Jordan study.

The consequences in the short run include better health care for Bedouin mothers and babies and increased schooling for Bedouin children. Some sons of Sheik Nayaf's followers in this village on the edge of the desert 25 miles south of Amman have gone to Britain, the United States and the Soviet Union to study medicine and law. Others are making more money than their parents ever saw, working for the government or the armed forces, and traveling every day to Amman in buses provided by the government.

The consequences in the long run are harder to evaluate. Bedouin traditions based on desert wandering have entered nearly every aspect of Arab life and language. Even in Lebanon, one of the most advanced Arab countries, one common way to say "please" alludes directly to the Bedouin custom of "entering" the territory of another tribe and asking for its protection. The famous Arab hospitality is, in fact, Bedouin hospitality.

Here in Jordan, Bedouin influence runs from King Hussein's dynasty through the civil service into the strong Bedouin foundation in the Army. In military parades, the Desert Patrol with its red-checkered headdresses, curved daggers and camel-riding gear always heads the procession in deference to the Bedouins.

The loss of this source of Arab culture seems bound to have an effect on the area over the years, although experts who participated in the study did not attempt to say what it would do.

One side effect in Jordan is to tighten supplies of meat, which traditionally had come from large sheep and goat herds maintained by the Bedouins.

The herds have now shrunk to an average of fewer than 10 heads to a Bedouin family.

"The demise of the livestock industry, more than anything else, indicates how much the traditional way of life has changed, as well as the inadequacy of the present livestock as a means of economic support," the researchers concluded.

Lt. Col. Dahash remembered how it used to be in his early days of patrolling the desert stretches in which he grew up. "You used to see them gathering around a water hole and there would be several hundred tents and thousands of camel calves," he said. "You should have seen it. But you won't see it anymore. Times have changed."

Under Sheik Nayaf's tent, the changes have made it possible for his son to walk into the middle of a consultation with troubled followers to ask his father for pocket money. In response, the sheik reached under his white robe and pulled out several dinars.

When some of his six sons went off into the desert recently to seek their roots on camping trip, Sheik Nayaf said they did so in a high-powered Range Rover. Things were simpler when he was a child, the sheik recalled.

Life there [in the desert] was good," he said. "The only things you had to worry about is where to pitch your camp for the night, and to be careful not to get into any disputes with anybody. But, at the same time, life in civilization is better. We have doctors and university graduates now.

"There aren't any real Bedouins anymore. We still have sheep. But now it's like America. They go to Amman and get feed and water and take it to them with tanks in a truck."

The University of Jordan researchers found that, like the sheik, most Bedouin fathers show little regret at seeing their children quit desert life for cities or villages.

"The men have a strong feeling that the life is anachronistic and unlikely to continue in the long run," they wrote. "Second, it seemed these fathers realized that the best future for their children could be obtained by moving closer to the modern urban sector and preparing their children through education and migration for jobs outside the desert.