Surrounded by the oil wealth that has transformed the lands around the Persian Gulf and by futuristic cities that seem to have sprung up over night, Ajman has retained something of the pace and style of the Arabian Peninsula's vanishing past.

Ajman is the smallest and poorest of the United Arab Emirates, the only one where nobody is even looking for oil, let alone producing it.

Many of its estimated 30,000 residents still live in modest one story houses, scattered about the sands and topped by traditional gulf wind towers. Even a few mosques are still not air conditioned, a rarity today in a country where summer temperatures can exceed 130 degrees.

Downtown Ajman consists of a few shops selling basics, not the lavish consumer goods emporiums that dominate the Gulf's richer towns.

Even the ruler, Sheik Rashid Bin Humayd Nuaymi, is a relic of a bygone era. A swashbuckling, white-beared figure who wers a hooked silver dagger, he was been in power since 1928, which is said to make him the world's senior hereditary ruler, and he spends much of his time reminiscing about the past.

With a land area of less than 200 square miles that is broken into three enclaves, no natural resources except some spring water and worst of all no oil, Ajman seemed destined to remain in the somnolent obscurity that marked its past. But Sheik Rashid and his son, crown Prince Humayd, who makes most of the decisions now, made a shrewd trade-off at the beginning of this decade that has brought their little land modest prosperity.

Of the seven sheikdoms that joined to form the United Arab Emirates when the British pulled out of the mitted to the federation, which is dominated by Abu Dhabi. Lacking the independent resources of Dubai or Sharjah, Ajman harbors none of their notions of independence.

Ajman backs the federation, which means total support for the policies of the president, Sheik Zayed of Abu Dhabi, and for the perpetuation of the union, from which more prosperous members occasionally talk of seceding. In return, Sheik Zayed has been generous.

"Abu Dhabi contributes wealth. We contribute dedication," Sheik Humayd said in an interview at his modest of fice opposite a plumbing supply store. "Wwe do not think of Ajman by itself. Our efforts go toward strengthening the union of the emirates."

Ajmanis, he said, "do not think of progress in local terms," which is quite a change from less than 10 years ago when Ajman guarded its frontiers and made most of its money issuing elaborate postage stamps.

"Fifteen years ago, when we went abroad and said we were from Ajman, people would get out a map and say, where's that?" he said. "Now we have international status. It's not just a question of roads and buildings."

But the infusion of oil money from Abu Dhabi has helped Ajman acquire those necessities, also, along with a few privately-financed industries. By the standards of Dubai or the other nearby emirates, Ajman remains a backwater, but in its own terms it has made dizzying progress.

"When I came here in 1967, there was nothing. It was a fishing village, maybe 4,000 people," said Adnan Dajani, a Palestinian who is director of Ajman municipality, a kind of hired mayor. "We have watched the tree grow."

The every limitations of Ajman's resources and ambitions, he said, have enabled it to avoid the development excesses that have turned neighboring Sharjah into an ultramodern ghost town.

Ajman has a new hotel, a color film processing laboratory, a dry dock that serves small vessels such as oilfield supply boats and tugs, and a plant built with French assistance for bottling its spring water. It is linked into the emirates' telecommunications, health and education systems, all of which are financed by Abu Dhabi's oil revenues.

An overambitious fishmeal plant was abandoned after construction had begun, and a local bank failed last spring when a banking crisis hit the entire country. But on balance, local analysts say Ajman's development has proceeded smoothly.

A promotional brochure prepared by Adjani's office said Ajman has "preserved the human scale of the town, its unhurried atmosphere and its relative quiet."

That partly reflects, Ajman's lack of land and funds, but Adjani says it is also partly by design.

"My plan, is to keep Ajman different," he said. "We have a few high rise buildings now but there are no more in the master plan. A modest villa is better than the concrete jungle."

The crown prince acknowledged only reluctantly that Ajman is beginning to face some of the same social problems besetting other parts of the gulf that have been suddenly modernized and brought into contact with new ideas. These problems exist, he said, but "are being solved by the federal government."