It is difficult to surprise the residents of the southern California coastal community of Malibu Beach. Living on one of the most celebrity-studded stretches of real estate in the world, they are used to just about anything.

Still, when Army trucks and jeeps began pulling up to Beach House #38 during the savage rains last March, residents stared in disbelief.

Did the Governor of California call out the National Guard, as some believe, to fill and pile sandbags just to keep Linda Ronstadt's $325,000 home from sliding into the sea?

Although the summoning of the Guard to Malibu enraged many homeowners who had to fend for themselves, the episode served to focus national attention on the intriguing and mysterious relationship between the two people involved...the Governor and the Rock Queen. Is Jerry Brown serious about the enchanting, raven-haired singer, whose name has been linked romantically with his for more than two years?

And is Ronstadt ready to settle down with the lean, handsome Governor of the nation's most populous state? After 14 years, Ronstadt, 31, has climbed to the top of her profession. She has sold more than 17 million albums, reportedly grossing $60 million on her last five, and has just made her movie debut ...singing in the just-released FM. If any motif dominates her career, it is lost love...a circumstance alluded to in her wailing hit "When Will I Be Loved?"

"All I've done in my music is acknowledge that I've been hurt," she told Rolling Stone magazine. "Ever since I was 6 years old, I've been looking for the perfect boyfriend. But I've wanted to sing since I was 2, and when it came right down to it, I could never give up singing for any old boyfriend."

Ronstadt and Brown met at Lucy's El Adobe, a Mexican restaurant in Los Angeles, when Brown was California's Secretary of State. They had much in common: their Catholic backgrounds, long experience in the public eye and familiarity with life on the road. When Brown launched his strong, if unsuccessful, bid for the Democratic presidential nomination in 1976, Ronstadt, along with fellow rock singers Ronee Blakley, Helen Reddy, Jackson Browne and Joni Mitchell, performed at his fund-raisers.

The friendship between the politician and the singer continued to grow. They were seen together at public events ranging from a recent tribute to Neil Simon at the Long Beach Civic Auditorium to a reception at the Beverly Wilshire Hotel for a group of Chinese diplomats. They've also shown up at rock hangouts such as the Roxy in Los Angeles. Last December, the Governor took Ronstadt to some of his old haunts in San Francisco: City Lights Bookstore, the landmark of the 50s beat culture, the Spaghetti Factory and the museums at the Academy of Sciences in Golden Gate Park. After touring the city in which Brown grew up, the couple went back to Malibu to spend Christmas together.

The friendship puzzles both Brown's supporters and his detractors. Is it a political ploy? Is it a platonic relationship? What does Ronstadt stand to gain?

The answer is unclear. Ronstadt and Brown avoid publicity when they're together. Photos of them with each other are all but impossible to get; they often arrive at and leave restaurants and nightspots in separate cars. And they both consistently refuse to shed any light on the relationship.

But the paparazzi are occasionally successful and are often the major source of tales about the couple's time together. One such report is that early last month they celebrated Brown's 40th birthday at the restaurant where they met. (The Governor likes Lucy's, located across the street from Paramount Studios, because he feels at ease among its celebrity patrons, many of whom are his political supporters.) After dinner, the two slipped out quietly. The next afternoon Brown was seen emerging from Ronstadt's house. He climbed into his chauffeured 1974 Plymouth Satellite and rode away. That night, they were seen dining together at Tony Rome's, another popular Hollywood restaurant.

Reports that the Governor spends weekends at Ronstadt's have surfaced frequently in the press, and apparently there is truth to them. Orville Schell, a writer who spent two years traveling with Brown in order to write a book about him, was at one point invited to Malibu. In his just-published book titled Brown (Random House), Schell describes a Saturday morning call to a number Brown gave him:

"Is Jerry there?"

"Just a sec," says a sleepy, female voice.

"Hi. What's happening?" says Brown a moment later, his voice in a lower, morning register.

 "Did I wake you up?"

"No, no, not really." A short time later, Schell found himself at Ronstadt's door, chauffeured there by the Governor's driver. Brown answered the door.

"Come in. Come in," he said casually, as if inviting me into his own house.

Brown and Schell discussed whether Ronstadt, clad in a jersey top and short shorts, and bouncing in and out of the room with coffee, should accompany them on a train ride with a delegation of Chinese from the People's Institute of Foreign Affairs.

"Maybe it's a little weird", Brown finally concluded, and the singer wrinkled her nose at being excluded. Later, Schell described the three of them wedged into Ronstadt's Porsche, Schell driving and Ronstadt sitting on the Governor's lap.

This all might be considered frivolous were it not for the central position marriage plays in American political life. The fact that Brown doesn't fit the stereotype of the family man hasn't affected his career. Although his voter approval rating has slipped somewhat from a peak of 87 percent in his first year (the highest in the history of polling in the state), he remains remarkably popular. Public opinion is not lost on President Carter's staff, which carefully monitors every move Brown makes. Carter aides characterize him as the "single largest threat" to the President's re-election in 1980.

But if the President is afraid of Brown, the Governor's staff has its own anxieties. Speculation that Brown is homosexual has persisted since political opponents first hinted at it in 1974 during his gubernatorial campaign. Brown denies that he's gay and points out, "Anytime you're a single person in politics, that's something people might say."

Veteran Brown-watchers believe there's no substance to the rumor. "He is 100 percent heterosexual," says Doug Willis, AP Bureau Chief in Sacramento, who was one of four reporters invited into Brown's office two years ago when the Governor dropped the bombshell that he was going to take a shot at the presidency. "You can tell", Willis says, "when, in the middle of conversation, you see a guy's eyes following someone in a skirt. You can't fake that after enough times."

Surprisingly, some of those who vouch for Brown's interest in women don't think his relationship with
Ronstadt is sexual. "I just think he uses Linda's home as a sanctuary. It's situated among an expensive group of houses that are guarded and closed off to the public," says Robert Pack, author of a biography of Brown called Jerry Brown: The Philosopher Prince, which was just published by Stein & Day. "His favorite pastime is walking on the beach. And he takes his privacy seriously...I don't think he would have a serious relationship with her because of her background, " Pack adds, referring to the numerous affairs Ronstadt has acknowledged having.

Last year, however, Ronstadt called domestic life "the richest thing in human experience. I really believe in the concept of the nuclear family", she told a newspaper reporter, "I don't have casual relationships. For me, they have to be serious."

Brown, too, says he hopes to marry someday, although he feels that at present, his political ambition would place too great a strain on a family. Perhaps he remembers the resentment he once voiced at being paraded before the public when his father was in office.

For now, a good deal of Brown's mystique derives from his bachelor status. In a recent Los Angeles Times poll, a 6-to-1 majority said they would like the Governor no better if he were married. Apparently there is something intriguing about a man who not only is single, but who spent three and a half celibate years in a Jesuit seminary.

Brown left the cloistered life in 1960 to pursue a legal career. He studied at Berkeley and at Yale Law School, and then returned to Los Angeles to practice law. He worked actively against the war and supported Sen. Eugene McCarthy's presidential campaign.

Brown climbed swiftly and easily to the governorship, assisted, he concedes, by the fact that he is a son of former Gov. Edmund G. "Pat" Brown.

Jerry Brown's youth and liberal background led to the belief that his tenure as Governor would be in stark contrast to that of his right-wing predecessor, Ronald Reagan. However, the first thing he told Californians was that they would have to "lower their expectations." He came down hard on crime, refused to raise taxes and said that in order to eliminate waste, he would examine all the departments of the state bureaucracy.

At the same time, however, he disdained the trappings of office, canceling the inaugural ball, refusing to live in the $1.5 million Governor's mansion Reagan had built, and putting the state limousine and plane into storage. But where, ask his liberal friends, are the job programs for the inner cities, the child-care centers, housing for the poor, tax reform? Brown answers their questions with questions of his own... offers esoteric quotes from Thomas Aquinas or dishes out Zen aphorisms.

He has moved in some new directions, however. He negotiated a landmark farm-labor law with Cesar Chavez, the growers and the Teamsters Union; he signed a law decriminalizing marijuana, a law ending oil depletion allowances and another permitting sexual freedom between consenting adults.

Even his political opponents grudgingly admire his style. "He's capable of taking the pulse of the public before the public even knows what it's feeling." said Paul Priolo in Atlantic Monthly. Priolo, leader of the Republican minority in the State Assembly, adds, "His philosophy is to do what's necessary to become President."

Harsher critics accuse him of cynical manipulation. They charge that the old blue Plymouth, the stark apartment, even his relationship with Ronstadt, are all calculated media ploys to further his career.

One critic suggests that the manipulation is more insidious. J.D. Lorenz, a former administration official, charges in Jerry Brown: The Man on the White Horse (Houghton Mifflin) that Brown developed a strong relationship with the large Mexican-American bloc in California at the expense of blacks.

There's one issue on which Brown openly bucked the public tide... the death penalty. His concern with capital punishment stems from his father's days as governor. He once called Pat Brown from Berkeley and persuaded him to grant a reprieve to Caryl Chessman, who was scheduled to die that night in the gas chamber. Last year, when a bill to reinstitute the death penalty came before Brown, and polls showed an overwhelming 70 percent of his constituents favored it, he was confronted with one of the toughest decisions of his political career. Brown vetoed the bill.

Few believe his decision will hurt his chances for re-election this year, particularly since the legislature overrode his veto. Although he won the governorship in 1974 by the narrowest margin in 50 years, it is difficult to imagine any challenger preventing his re-election.

Aides say Brown comes alive before a crowd. The words flow, "buzz words " Lorenz calls them: "my solar energy plan"; "a state space program"; "a better climate for business"; "property tax relief."

Brown has had one term as Governor of a state whose budget is topped by only five nations in the world; he spends weekends with a beautiful rock star...and he seems more anxious than ever to take on Carter in 1980. Yes, under the warm California sun, it even seems possible to imagine Linda Ronstadt as First Lady.