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EVEN FOR A SEASONED WORLD TRAVELER like Peter Jennings, it was a memorable homecoming. In July the newsman, split since last August from his wife of 15 years, author Kati Marton, stepped off a plane after returning from Haiti, only to discover that he himself was the news -- because of his presumed romance with Barbra Streisand. The dashingly eligible Jennings, 56, says a colleague, "was stunned." !

Oh, sure, the anchor and the diva had looked the perfect couple -- he in white tie, she in shimmering silver Donna Karan gown -- when they attended the Clintons' first state dinner together at the White House in June. And true, a few weeks later, Streisand, 52, stayed into the wee hours at Jennings's Bridgehampton, N.Y., summer house, helping him clean up after a dinner party before leaving to spend the night at Karan's home nearby. Still, was this really a romance, or was it Barbra's habit of, as one source says, "fixating like a laser beam" on people whom she was interested in?

It's true that for Streisand, Jennings is that hard-to-find suitable object for her attentions, which have included calling the anchor to say she liked the white shirt he wore one night on the evening newscast. "She loves meeting fascinating people," says a friend of the singer. "God knows he fits that bill. Sometimes it's very hard for famous people to meet others."

It may be hard to feel a lot of sympathy for those who seem to have everything. But imagine for a moment that you, like La Barbra, are rich, famous and fabulous. Imagine, too, that like more ordinary women you have a simple desire: to meet a guy who is well-groomed, well-informed and, well . . . possible. Theoretically there should be no problem. But the reality is often heartbreakingly difficult. According to a range of celebrity women who have lived to tell their tales, it can be surprisingly hard to be single in Hollywood. The stars may get to go to a better class of restaurant, but for the famous the usual levels of fear, paranoia, longing and anxiety that accompany the search for true love -- especially for those thrown back into the search after being happily hitched for years -- are ratcheted up several notches and on public display. Even Sharon Stone, who never seems to be hurting for male companionship, complained that the men who see her on the screen "make up an idea of who you are. They don't take the time to find out. They think they know what you're all about."

For those who suddenly find themselves flying solo after years of married life or long-term relationships, the Hollywood dating scene can be absolutely devastating. Melanie Griffith, who separated from Don Johnson a few weeks before he entered the Betty Ford Clinic for treatment of alcoholism and abuse of prescription drugs last June, said recently that the single life "is sad, and it's wonderful." Singer Paula Abdul, after filing for divorce in May from Emilio Estevez, her husband of two years, "threw herself into her work," according to a friend. But Abdul, at a vulnerable moment in her life, is also now being treated for an eating disorder at the Laureate Psychiatric Clinic and Hospital in Tulsa.

Then there is the more classic case of Sally Field. The actress and her husband of nine years, Savoy Pictures head Alan Greisman, first separated in January before she filed for divorce last month. Since then, Field, 47, has worked hard on an upcoming TV movie and won praise for her portrayal of Tom Hanks's weary-but-wise mother in the hit movie Forrest Gump. But for now, the only men in her life are her sons, Peter, 25, and Eli, 22 (by first husband Steve Craig), and Samuel, 6.

Why is the Hollywood dating game so hard to play? The answer lies, ironically, in the very things that the stars want most: money, fame and attention. As director Penny Marshall said, "In this business there's a lot of pressure. Someone's working, someone's not working, egos are bent out of shape." And when women reach the top of the heap, they often find, unfortunately, that they have a wonderful view of slim pickings. Joan Rivers says that for two years after her husband of 23 years, Edgar Rosenberg, committed suicide in 1987, not one person asked her out on a date -- and on New Year's Eve, when people assumed she had plans, she often wound up staying home alone. ''They all think you're waiting for Clark Gable to call,'' explains Rivers, 61, who is now seeing Orin Lehman, 72, a retired New York State parks commissioner.

Perhaps no celebrity understands the difficulties of mixing fame and love better than Whoopi Goldberg. She was not generally seen as an object of desire, she said recently, until she began dating Ted Danson. "That kind of woke people up," she said, adding that she knew people were wondering, "What's he doing with her?" Though she has said that their romance had faded before Danson's fiasco in blackface at a Friars Club roast last October, Goldberg has confessed that the breakup was -- and still is -- "devastating. It was real painful and it was very public."

Goldberg has managed to move on. When she was asked recently by a reporter for USA Weekend how she dealt romantically with men, she said, "If they're secure, it's easy." After Danson, she says, she was determined to steer clear of that notably insecure group of people, her fellow movie stars -- and perhaps to find someone not intimidated by the fact that she reportedly commands $8 million per movie. "Money is a heavy thing," explained Goldberg, who is engaged to Lyle Trachtenberg, a union organizer she met on the set of Sister Act 2. "Fortunately, I've found someone who doesn't quite give a damn about it."

In Hollywood, where everyone is either on the way up or the way down, many stars admit they must also be wary of hangers-on looking for a quick ride to the top. "I was at a party once and a young man came up to me and said that he had always wanted to go to Saint-Tropez," recalls Rivers. "I said, 'Good for you. Why don't you go? Au revoir.'" Catherine Bach, 40, who divorced her first husband, David Shaw (stepson of Angela Lansbury), during her six-year run as Daisy Duke on The Dukes of Hazzard, agrees that she never knew what men's motives were for pursuing her. "Before, I knew everybody liked me for myself," says Bach, now happily remarried to lawyer Peter Lopez, 44. "Then people dated me for who they thought I was, and I would think, 'They'll stop liking me when they find out who I really am.'"

Griffith, since breaking up with Don Johnson, has spoken about receiving a bruising lesson in the difference between real and phony friendship. "The people that I thought were my friends ((in Aspen, where the couple lived)) were not," she said. Most turned out to be "more interested in my husband than in me -- they would want to be close to me in order to be closer to him." Soon after the couple split, Griffith, 37, was seen around Hollywood for a few days with businessman Bryan Kestner, 28, whom she teamed up with at a Planet Hollywood party in July and who had previously squired actresses Julianne Phillips and Emily Lloyd and model Jill Goodacre. But soon Griffith retreated to the Hamptons for the summer with her two children, Alexander, 8, and Dakota, 4.

Abdul, 31, though separated for three months, has most definitely not reentered the celebrity social whirl. Instead, she is finally coming to grips with the bulimia that plagued her even before her 1992 marriage to Estevez. The 5 ft.2 in. former L.A. Lakers cheerleader's weight has reportedly fluctuated some 20 or 30 pounds, and for years she has attended meetings of Overeaters Anonymous. ''She's really looking great,'' says someone close to her. ''But the problem is that she looks in the mirror and sees a fat person.'' Now, with Estevez out of the picture, Abdul, says a source, is ''trying to take care of something that's been a problem for her. She wants $ to be healthy and stay real positive.''

It's a bit harder to sympathize with the problems of some solo women -- those who simply seem too beautiful to ask out. Model Jennifer Flavin, 25, now dating Australian media mogul James Packer, 27, complained that after her highly publicized breakup with Sylvester Stallone, ''a lot of nice guys were afraid to come up to me. It's usually the cocky ones who do -- men who just want to have a woman like me on their arm.'' Even TV vixen Heather Locklear, 32 -- now happily involved with Bon Jovi guitarist Richie Sambora, 35 -- found it rough going at first when she split from her husband of seven years, Motley Crue's Tommy Lee, in 1993. ''I didn't get a lot of calls from guys after people found out I was getting a divorce,'' she says.

Sally Field seems to be coping with her pending divorce by being too busy to take any calls that might come. The Oscar-winning actress is currently in Houston, where she is filming the aptly titled A Woman of Independent Means, an NBC miniseries of which she is executive producer and star, and which is scheduled to air early next year. ''I don't feel any sort of dampening to my appetite,'' she said recently about the thrill of her work. ''I'm as eager to go on to the next thing as if it were the first.'' And she is using her family as an anchor. Field has rented a five-bedroom brick house near Rice University, which she selected in part so that her sons -- Peter is a production assistant on the movie, Eli visits regularly from Boston and Samuel is close by his mother's side -- could play tennis and soccer and go swimming. ''Particularly in times of trouble, her boys are always helpful to her,'' says one Houston acquaintance. ''They are certainly No. 1 to her.''

But Field, whose early Hollywood dates included Johnny Carson and Burt Reynolds, is, after all, human, and she recently confided to a friend that she had no idea how or where to meet a man. ''Most of my friends ask me about her, and I just say she's like any of my other 47-year-old friends,'' says the acquaintance. As for Field's romantic life, the Houstonian adds, ''We all live that through our children.'' (In fact, Field could get a date if she really wanted one -- with, among others, attractive local KTRK weekend weatherman Frank Billingsley, who says he once asked her out in 1975, when he was about 15 and making a prank phone call. Billingsley, now 34, recently took to the airwaves and, he says, ''told her to call me. I like her, I really like her.'' So far, no luck.)

So where do unattached stars find true love? If you're Kim Basinger, Susan Sarandon, Jessica Lange or Goldie Hawn, at work -- with, respectively, Alec Baldwin, Tim Robbins, Sam Shepard and Kurt Russell. You're on location and stuck there for three or four months. Sometimes celebrity itself brings people together. Diane Sawyer and Mike Nichols met eight years ago in an airport waiting room in Paris. ''They were both famous,'' explains an acquaintance of the couple. ''If you're famous enough, you can say 'Hi' to another famous person. You're already part of the family.''

Another tactic is for an actress to ask her agent to ask another client to escort her to a big event like the Oscars or the Emmys. ''Madonna doesn't go to the dry cleaners, which is where everybody else goes to meet men,'' says Liz Rosenberg, the star's publicist. ''Stars tend to be pretty removed from the world.'' Maybe not all of them. Dr. Joyce Brothers, widowed in 1989 after 39 years of marriage, resorted -- without much luck -- to a method thousands of women before her have used: She answered a couple of personal ads in New York magazine. ''Personal ads are dangerous,'' jokes comedian Rita Rudner, happily married to Peter's Friends cowriter Martin Bergman. ''You have to separate the ones who are lying from the ones who are hallucinating.''

And like mere mortals, some stars even have good friends with other well- connected friends. Wendy Goldberg, a former marketing consultant for Revlon who is married to former Twentieth Century Fox head Leonard Goldberg, loves to throw intimate dinner parties to which she invites a liberal sprinkling of highly successful men and women. In July, Alana Stewart (ex of Rod Stewart and George Hamilton), Tina Sinatra, Jackie Collins and Brenda Richie (ex of Lionel) dined on Caribbean food at the Goldbergs' Bel Air home along with writer-producers Tom Mankiewicz and Seth Perlman, as well as Neil Simon and his wife, Diane.

Getting a date, of course, is only half the battle for a celebrity. ''Could your relationship withstand constant scrutiny?'' Don Johnson's publicity agent, Elliot Mintz, recently wondered. ''I know mine couldn't.'' Sharon Stone would agree. When asked what she misses most now that she is famous, she answered, ''Being able to kiss someone I like and not have to worry about its being in the newspaper.''

Of course the single life is not all misery, loneliness and pints of Cherry + Garcia ice cream in front of the TV. Madonna, says Rosenberg, ''has a pretty regular life. She's not desperate, and she's not going out with 18 NBA players at one time.'' Twice-married Glenn Close -- the actress, let's recall, who made single a synonym for monster in the movie Fatal Attraction -- has spoken recently of her reordered priorities: her 6-year-old daughter, Annie, and her work. ''I'm finally the head of my own compound,'' she explained. ''I've learned everything the hard way.''

And though she has a steady beau now, Rivers has also learned to recognize some of the joys of being single. ''You live your own life, you're making your own way, and you don't have to fight about what color the carpet is,'' she says. ''That's the best of all possible worlds.''