Headquartered on opposite sides of the country, one in Tel Aviv and the other in Jerusalem, two Americans who lurked in the background of Israel's national election became known simply as "the hired guns."

David Garth, the gregarious New York-based political consultant who has advised U.S. political campaigns of presidential aspirant John Anderson, New York Mayor Ed Koch and Los Angeles Mayor Tom Bradley, moved into a suite in the King David Hotel here to work with Prime Minister Menachem Begin in his bid for reelection.

Davis Sawyer, best known for running political campaigns for Sen. Edward M. Kennedy and a long list of gubernatorial candidates, based himself in Tel Aviv's Dan Hotel, from where he advised Shimon Peres, the opposition Labor Party candidate.

It was the first Israeli political campaign in which American image-makers and strategy consultants were imported, and Garth and Sawyer appear to represent a burgeoning new American industry -- exporting political savvy to foreign election campaigns.

Both refused to talk for quotation during the campaign, for fear of upstaging their Israeli clients, but in interviews after the election on Tuesday each offered his insights into the strategic maneuvering of the campaign.

Garth and Sawyer said much of their effort involved "guidance" in campaign media work. This was particularly concerned with each party's advertising agency and the film company producing television spots that were shown nightly on Israel's single state-owned channel.

Israeli campaigns entail relatively little barnstorming by candidates. Most of the emphasis is placed on television and efforts to capitalize on campaign-generated controversies and charges and countercharges about performance and suitability for office. All of this is closely followed by Israel's aggressive news media. The consultants said that a healthy respect for American media wizardry during campaigns probably prompted the Israelis to look for outside help this year.

Garth has worked on campaigns in Venezuela and Bermuda as well as this one, and Sawyer has taken his talent to Costa Rica, the Dominican Republic and Venezuela. The two faced each other in Venezuela, where they lent a kind of backroom American aura to the distinctively Latin campaign.

"For years, politicians around the world have been going to the United States to look at our political campaigns. It was inevitable we would start working abroad," said Garth, who controls a network of campaign consulting firms. Garth-Furst Inc. has the contract with Begin's Likud Party, and Garth's partner in this campaign was Zeev Furst, former director of the Anti-Defamation League here.

Garth bristles when people suggest he is offering prime ministerships to the highest bidder.

"That's crazy," Garth said. "The Labor Party approached us two years ago, but I wouldn't work for them on a bet. One meeting with Peres convinced me of that." He said he also met Begin two years ago and liked him immediately.

"I heard all the stories about him and saw all the bad press," he said. "In a crowd, he's a real orator. He turns them on. But alone, he's a cool, logical guy who is really interested in how the campaign is being put together."

Sawyer came here in November to work Labor Party leadership against archrival Yitzhak Rabin, the former prime minister. When Peres beat Rabin in the party's national convention, he asked Sawyer to come back for the general election.

"The problems were unbelievable," Sawyer said. "Here's a party that had been voted out in 1977, and for all the reasons for which they were voted out, they became obsessed with internal problems."

Labor's internal struggles often made it difficult for Peres to take clear positions, with the party's policy committee frequently splitting over key campaign issues and then compromising on a public stand that appeared ambiguous.

Peres, whom Sawyer calls a "decent nice guy with a lot of good ideas for solving Israel's problems," also was afflicted with a personal-image problem. Many Israelis viewed Peres as a shifty, less-than-trustworthy backroom politician who for years had undercut the highly popular Rabin. it was the campaign staff's job to transform him in the public's eye to a responsible, moderate, level-headed leader standing in stark contrast to a precipitous, unstable and messianic Begin.

The campaign got off to a rocky start for Peres, who was forced to watch as Begin took command of events, shifting attention from the domestic issues on which he was most vulnerable and adopting a popular, hard-line position on the deployment of Syrian missiles in Lebanon and the bombing of Iraq's nuclear reactor by Israeli warplanes.

To deal with Begin's domination of the campaign, Peres' advisers adopted a strategy of attacking Begin's judgment on national security, while at the same time holding him personally responsible for the wave of election-rally violence that had marred the campaign. The idea was, Sawyer said, to bait Begin into extreme rhetoric and thus frighten voters away from the Likud.

"It worked," Sawyer said. "Begin played right into it, but it was just a little too late for us. We needed a week or so more." Largely by making Begin the central campaign issue, Peres closed the gap from the 37-49 parliamentary-seat deficit predicted in pre-election polls to a 49-48 victory in the vote, even though the result appeared to fall short of preventing Begin from forming a coalition government.

Garth said he, too, faced problems when he joined the Likud campaign team.

"Things always look dismal when we come in, but we were really underdogs this time," Garth said, citing Begin's low standing in the polls in January, when the government faced collapse. But, Garth said, Begin was able to project himself as a strong leader during the crises over the missiles and the reactor, while at the same time solidifying his support from the 53 percent of Israel's population that is Sephardic, a term that describes Jews from Africa or Asia.

"The election ran on ethicity," Garth said. "The Labor Ashkenazim [Jews of European origin] said, 'We built this country,' and the Sephardim resented the hell out of it."

Both of the American consultants said they were surprised by the intensity of Israel's rough-and-tumnble campaigns.

"In the United States, we're in a daisy chain compared to here," said Garth, citing one pro-Labor television program that alternately flashed scenes of wildly cheering Likud supporters with shots of Nazi Party rallies in pre-war Germany.

Sawyer, who said he had seen some tough campaigning in Venezuela, said, "They play hardball here."

Garth and Sawyer each emphasized that he acted as a consultant, offering advice and not running the campaigns or dictating strategy.

They also said that their paths never crossed during the bitter, three-month-long campaign.

With the disdain for a political rival that goes naturally with a heated campaign, Garth said, "Most of the time we've gone against Sawyer, we've appreciated having him on the other side."

Said Sawyer of Garth at one point in the battle, "I don't know what he's doing over there. I don't think anybody can tell Begin what to do."

For their part, the Israelis involved in the Likud and Labor campaign organizations seemed to take the non-Hebrew-speaking American "hired guns" lightly.

A Begin confidant who was elected to parliament on the Likud ticket said that the $5 million allotted to the parties under Israel's generous campaign financing law -- more per capita than is spent even in U.S. elections -- allowed both the Likud and Labor the luxury of splurging on expensive American consultants. When one party saw the other hiring a ringer, he said, both had to have them.

"We know how to run campaigns," the Israeli said.