Dwight Eisenhower was the first important guest to cross the threshold. Presidents and princes have been stopping by ever since.

Now it's apparently the shah of Iran's turn to visit the 250-acre oasis which Walter Annenberg's millions began carving out of the California desert a dozen years ago -- although, according to Ambassador Ardeshir Zahedi last night, the shah's visit to the United States is being delayed, as the tense maneuvering for political control continues in Iran.

"I don't want to see one grain of sand except in golf traps," commanded Annenberg, the Philadelphia publishing potenate and art collector long before Richard Nixon named him U.S. ambassador to Great Britain. Commanded, apparently, with some success.

Today, the L-shaped spread is bounded by mature, sometimes rare, trees and shrubs, a redundancy of emerald fed by a dozen man-made lakes and interrupted only by topaz traps of sand.

Sprawling there on the doorstep of Rancho Mirage, a 20-minute ride from Palm Springs in the vast Coachella Valley that has been the desert song of rich men since the 1930s, Annenberg's Sunnylands is a marvel of what one man and his money can do in another man's wasteland.

Persepolis it is not. Niavaran Palace it is not. A port in the political storms raging in distant Iran it unmistakably is. A refuge with its own security system, its own helicopter pad, it's own support staff, it is as fit for a Pahlavi as it has been for a Windsor, a Nixon, a Ford, an Agnew.

A fiefdom, even, flying its own golden stylized Mayan sun god on a field of white -- just below a fluttering Stars and Stripes -- it has been modestly reassessed for $3.8 million by Riverside County in the wake of Proposition 13. It is a mere shadow of its original 900-acre self, nearly 700 of them having been sold off by Annenberg in December 1977, for $10 million, cash.

The main house with its soaring 38-foot living room ceiling, is a one-bedroom museum of French Impressionist paintings, stunning and rare sculptures, porcelains, jades and enamels. There are specimen flora on the grounds and in the greenhouse as precious to Lee and Walter Annenberg as many of their art works. And with its two satellite four-bedroom guest cottages, there is a staggering expanse of living space that totals nearly 33,000 square feet.

"Anyone who is in California or the entire Western Hemisphere would kill to get an invitation there," exclaimed Town and Country magazine's Nancy Holmes after a rare -- for journalists particularly -- invitation to visit.

There is little doubt that an over-night stay is an experience, or that a stay of several days with golf, swimming and tennis-anyone is comparable to a vacation at one of the world's poshest resorts.

"There are nice touches," says Nancy Hoving of the Annenberg's hospitality. "They leave a list of people staying there at the same time you are, and a schedule of what's going on."

Staying there at the same time as Nancy and Thomas Hoving, former head of the Metropolitan Museum of Art, were author Michael Grant, multimillionaire art collector Charles Wrightsman and Philadelphian Henry McElhaney.

Guest cottages lack few -- if any -- amenities. Kitchens have hot-and cold-running water, stocked refrigerators and there are maids to cook breakfast in case nobody wants to rough it.

"We didn't want her," remembers one Annenberg friend, "but we didn't know how to get rid of her."

The Hovings apparently had no such problem but, she recalls, "obviously what people like is to be fed when they're hungry and not have to go into the kitchen to do it, if that's their style. It's all so deceptively simple."

Golf, tennis, swimming and the main house are a golf cart away; lunch usually al fresco, dinner sometimes grand, sometimes informal.

"The women all tend to wear their Givenchys and Balenciagas," says Nancy Hoving, "though the Annenbergs claim it's informal, and the men wear blazers."

Like their Quincy Jones-designed house the Annenbergs are "not at all ostentatious, terribly, terribly well done," says a friend -- and they have an international reputation for entertaining graciously.

"They're a very well put-together pair," says Nancy Hoving. "It takes an awful lot of money to do things in the right way."

Long a friend of Ambassador Zahedi, the Annenbergs were guests of the shah and his empress in Tehran. Annenberg invited the shah's mother and sister to take refuge at Sunnylands recently when he read of demonstrations against them in Beverly Hills. He extended a similar invitation to the shah as a gesture of what he called "reciprocity," according to a Palm Springs journalist.

If some friends are wondering how long the shah will stay, at least one friend is certain Annenberg has everything under total control.

"He and Lee love their life there," says a friend. "They are being very generous. But they'll go just so far. Some idiots would turn over the key but the Annenbergs will give the shah time to catch his breath and then..."

Annenberg, himself, has described the shah's stay as a "temporary" one.

Palm Springs residents are hardly clearing their engagement books. "They say," says Mrs. George Hearst, Patty's aunt, "there's not going to be any kind of socializing."

Nor is anyone expecting much to come of rumors that the Pahlavis might be house-hunting in the area if and when they arrive from Morocco. The shah's style, says another long-time Annenberg friend, is more in the realm of Sunnylands.

"I remember the very first time I saw it, "says the Philadelphia lawyer. "I said to my wife, 'There are only two people in the world who could have built this -- Walter Annenberg and the shah of Iran."