This is the making of Hair Wars.

In one corner, Julius Bengtsson, hairdresser to the first lady, wearing a lavender Ralph Lauren polo shirt and pleated trousers. He often puts a dip in the front of Mrs. Reagan's hair.

In the other corner, Marc de Coster, known as Monsieur Marc, first hairdresser to the first friend of the first lady, Betsy Bloomingdale. He works in a long-sleeve shirt and silk tie. He goes for the wispier, softer coif.

Scene of the action: the royal wedding in London.

At stake is the hairline that makes headlines. Both Julius and Marc want to fix Mrs. Reagan's hair during the several days of wedding festivities.

And the tension of the dilemma is such that the other day Julius remarked, after sculpting in the soft plaster his signature hairstyle on the mannequin that will represent Mrs. Reagan in the exhibit of first ladies' inaugural ball gowns at the Smithsonian: "I wish it was Marc's head I was sculpting." Julius gestured as though slipping a knife across the jugular.

Julius has doe Nancy Reagan's hazir for years -- and occasionally, in California, has clipped the president. He is responsible for Mrs. Reagan's hair color -- chestnut brown with blond highlights -- and created that much-talked-about swept-up hairstyle she wore to the inaugural balls.

Marc has been doing Mrs. Reagan's hair on her New York visits since they were introduced by Betsy Bloomingdale (who also has introduced Mrs. Reagan to Adolfo suits and alligator handbags by Judith Leiber).

California-based Julius' clients include Hollywood and television biggies like Dinah Shore and Zsa Zsa Gabor, plus many of the Reagans' oldest friends. Julius often follows the stars on assignment, and when his trips east coincide withthe visits here of Mrs. Reagan's girlfriends, he takes out his comb.

Marc, whose salon is on the Upper East Side, used to do the duchess of Windsor's hair, and also Babe Paley (with whom he traded recipes) and Pamela Harriman.

But they have saved their best cuts for each other.

They are now both in London, Marc left on his own last week on a commercial flight. Julius stayed overnight at the White House before leaving yesterday with Mrs. Reagan on Air Force One. He will stay at Winfield House, the U.S. Embassy residence in London.

Julius' mission: to comb Mrs. Reagan's hair twice daily.

EXCEPT . . . except for one night when Marc will take over the responsibility.

A total surprise to a crestfallen and worried Julius.

Word that Marc was getting this heady opportunity came through Marc's press spokesperson. In reporting that Mrs. Reagan was about to have her hair done in New York last week by Marc's assistant since Marc was in London, she mentioned, by the way, that Marc would be doing Mrs. Reagan's hair in London one evening.

The White House has confirmed the news, although it wasn't sure, either, just what evening it would be.

Julius learned only Wednesday, after his work at the Smithsonian, that Marc would be cutting out a share of his work in London. But Julius really doens't have to worry. He doesn't like to say it because he doesn't like to give away his age, but he's been doing Mrs. Reagan's hair for more than 15 years. (Another age giveaway: He recently took down a picture in his bedroom autographed from Marilyn Monroe with "Julius, it is memorable flying with you. Anytime, Marilyn.")

Julius has done Mrs. Reagan's hair for all crucial occasions -- inaugurations, television interviews, photo sessions with Vogue and the like. And he has traveled with her before, including President Reagan's first official visit outside the country, to Canada. He learned well from that trip and this time packed a tuxedo with his London luggage. "I couldn't go to a formal dinner in Canada and had to stay in my room eating jellybeans," he laughs.

And Julius is well prepared for London. Although Winfield House has facilities for taking care of Mrs. Reagan's hair, he has ensured that the right stuff will be there through the international offices of Clairol, for which he is consultant. And he's got backup equipment packed with his suitcases. And ingratiating himself further, he'll offer to do the hair of Mrs. John J. Louis, wife of the American ambassador in London, while staying in the residence.

Meanwhile, Marc has made some effort to cool the feud, first inviting Julius to dinner at the Jockey Club during the inauguration ("Not dinner -- drinks," says Julius). Then Marc tried to greet Julius recently in New York, where Julius was judging a hair-design competition. "I saw him just as I was closing the door of the telephone booth," smiles Julius about the brushoff.

"When I was doing her [Mrs. Reagan's] hair in Pacific Palisades, it wasn't like this. No one else claimes they were doing her hair," said Julius. "I thought Hollywood was a tough place. I though Dinah Shore and Zsa Zsa Gabor were the big stakes. I'm not a fighter, but I guess I'm in the big ring."

Says Marc philosphically, reaching for a metaphor: "I always thought it was nice for a woman to have two lovers."