Maureen Gawler, private eye, has a nickname after nine years in the gumshoe business.

"Some of our clients like to call me 'The Butcher,' " she beams.

" 'The Buzzsaw,' " her partner, John M. Flatley, interjects.

"What?"

" 'The Buzzsaw,' " says Flatley. "They call you 'The Buzzsaw.' "

"I thought it was 'The Butcher.' " Gawler looks slightly wounded.

She is not miffed at her partner. In fact, she adores him. In private eye circles she is known more fully as Maureen Flatley Gawler, and Flatley -- retired G-man turned sleuth-for-hire -- is her father.

Based in the Maryland suburbs, they form a rare father-daughter investigative team, specializing in executive protection, "employe integrity" (also known as stealing), "loss prevention analysis" (preventing stealing) and sniffing out the dirt in big-time business deals, especially mergers and takeovers. Most of their work comes through word of mouth.

"I won't do divorces," says Flatley. "Too dirty. I won't peek in a window."

After a mid-1970s divorce of her own, Gawler, with two small children and no clear idea of what she wanted to do, eased into working for dad. "Every once in a while he'd have something I'd fit the bill for," she says, "when he didn't need a man in a Brooks Brothers suit and a snap-brim hat."

The two hit it off famously. Their professional relationship is part love, part respect and a very frank exchange of opinions.

"I can't remember when we agreed initially on any issue," says Flatley amiably. "You know, 'let's compromise and do it my way,' " adds Gawler, smiling.

Flatley lives in College Park, Gawler in Rockville. They work out of their homes and have unlisted telephones. Flatley says they call to check on each other every day, for security reasons.

"We do not," Gawler interrupts. "You call to bug me . . . . He leaves terrible jokes on my answering machine."

Their partnership is sufficiently rare that they wonder whether it might make a good TV series. More to the point, they wonder whether it already has.

There are striking similarities, Flatley and Gawler say, between their experiences and ABC-TV's "Eye to Eye," a new private-eye show starring Charles Durning and Stephanie Faracy that airs on Channel 7 at 9 p.m. tonight.

Two years ago, according to Flatley and Gawler, they were visited by actor Ralph Waite, who earlier had played the father on "The Waltons." They say Waite was developing programs for Warner Bros. television, creators of "Eye to Eye."

"We spent almost a whole day with Waite," says Gawler. "He asked a million questions about our lives. How my kids dealt with it. What it was like working with dad. The essence of it, not the details of their cases ."

Gawler says Waite was interested in "a retired federal-type investigator working with, perhaps, his daughter as private eyes."

No one gave it further thought until "Eye to Eye" debuted March 21.

In the show, Durning is teamed with the daughter of his deceased partner, played by Faracy. Faracy drives a baby blue Mustang convertible as, says Gawler, did she. Faracy's character is named Tracy; so is one of Gawler's daughters.

Before getting into the business, Faracy's character was a florist. So was Gawler. And the age difference between Durning and Faracy rivals that of Flatley, 63, and Gawler, 36.

So is "Eye to Eye" based on Flatley and Gawler?

"No way," says the show's producer, Michael Elias. Elias says the series grew out of a Warner Bros. movie "The Late Show," starring Art Carney and Lily Tomlin.

Any claim of similarity "doesn't come close," says Elias. "Not one bit."

Gawler insists she doesn't care about the money; she simply was amused when she called Warner Bros. recently and was referred immediately to the legal department.

Warner Bros. television confirmed yesterday that Waite had a development contract with the company between July 1981 and September 1983. Waite could not be reached for comment.

The work-a-day world of Flatley and Gawler is distinctly un-Hollywood -- no car chases, no surveillance and no gun fights, although Flatley owns a gun.

"I really have an aversion to them," says Gawler. "There's a real emphasis placed on weaponry when, in fact, finesse is your greatest tool . . . .

"The business in general has gravitated away from the rumpled trenchcoat and the binoculars on the car seat."

Gawler says she was struck at an early age with her father's "absolutely fascinating" 21-year career in the FBI.

One tale recalled by both involves the late Joseph Valachi, a convicted Mafia hit man whose Senate testimony in the 1960s helped blow the lid off organized crime. Flatley was in charge of Valachi at the D.C. Jail at the time.

On Valachi's birthday, Gawler baked a cake and Flatley delivered it.

"Did your goil make this for me?" asked the veteran underworld murderer. "Where's da file?"

In Gawler's eyes, she says, her father was hero material: "I thought he could fill up the bathtub and walk around on it." She says working with him now is "so fun. We have such fun together." And that includes the fights and friction. "He's usually the conservative," she says, "and I'm 'let's go for it.' "

She frets that Flatley often performs work gratis for old FBI friends. "He's the one who won't send the bill," she says. "He has this great FBI pension. I have a mortgage. I tell him, 'I don't care if you know him. Send the bill.' "

They cheerfully acknowledge that they scream at each other a lot on the phone.

Gawler handled a call from a client in New York who wanted to know what it would take to launch an investigation by the Securities and Exchange Commission.

She says she checked with a source at the SEC, called the client back and said: "A rumor."

"The guy never called dad back."

Still, neither partner would have it any other way, says Gawler. "We're really pals."