The crowd that gathered under the hot afternoon sun in a dusty playground in Tel Aviv's Yemenite Quarter gradually rose to meet the emotional pitch of the voice booming over loudspeakers with promises to rid Israel of Arabs "like bug spray on these cockroaches."

"When they heard Kahane was in Ramallah," Rabbi Meir Kahane shouted, referring to his Army reserve duty in that West Bank city several years ago, the Arabs "crawled out on their hands and knees."

"Kahane! Kahane! Melech Yisrael!" the crowd chanted, raising clenched fists in the symbol of his Kach Party. "Kahane! King of Israel!"

Kahane's voice rose higher: "Whatever Arab came in on a truck goes out on a truck. Whatever Arab came in on a donkey goes out on a donkey." And the crowd chorused, "Kahane to power!"

Standing in the audience, Bentsi Margolin, 17, who will enter the Army next year when he finishes high school, said, "He's doing exactly what needs to be done, so that we'll be able to live in peace and not be afraid to go down the streets."

"There are a lot of Arabs who say nice things about Jews in public, but in their hearts they'd really like to stick a knife in your back," Margolin added.

"The Arabs have to know who runs this country," said Tiran Capilot, 18, an auto mechanic who will enter the Army in four months. "I think he is the right medicine. Maybe a bit drastic, but the right medicine."

The two teen-agers, and others interviewed, reflected what many moderate politicians and leading social scientists see as a serious social problem facing Israel -- a drift by the country's burgeoning adolescent population toward radical right-wing ideologies.

Motivated by growing fear of a new brand of spontaneous terrorism against Jews in Israel and the occupied territories by Palestinian nationalists, and by self-doubts from the costly war in Lebanon, increasing numbers of Israelis who previously identified themselves with the rightist Likud policies of former prime minister Menachem Begin and former defense minister Ariel Sharon are now openly allying themselves with the extreme anti-Arab views of Kahane, according to leading public opinion analysts.

The trend not only has caused concern in the mainstream center of Israeli politics, but is causing increasing worry in the Likud bloc and among its still allied splinter factions, which once were considered to be on the irrational fringes of the ideological spectrum but now have been moved closer to the center, losing electoral backing to Kahane in the process.

Kahane's brand of open race-baiting still is attractive to only a distinct minority in Israel and is widely condemned by the majority of Israelis. But all leading public opinion analysts here agree that if elections were held now, Kahane, who holds only one seat in the 120-member Knesset, the Israeli parliament, would win five or six seats for his party, virtually assuring it of a pivotal role in any conservative coalition government, and that his influence is growing.

Citing a recent poll by the Public Opinion Research Institute indicating that 10.6 percent of Likud voters would vote for him -- and estimating that he would win 9 percent of the total vote, or 11 seats in parliament if elections were held now -- Kahane said in an interview, "We have a tremendous chance of being the third-largest party. That is a revolution itself, and every week that passes gives us more seats."

Opinion analysts and advisers close to Prime Minister Shimon Peres, who until recently laughed off the Kahane phenomenon as an aberration, now admit privately that his movement has acquired momentum, and they say it is the most disturbing social trend in recent memory.

In a step clearly aimed at stemming Kahane's growing influence, the Knesset last month passed a bill banning from parliamentary elections any party that incites people to racism or negates Israel's democratic character.

Kahane, who was temporarily ejected from the parliament that day for inflammatory statements and did not vote on the bill, said he would counter it by drafting a platform consisting solely of passages from the Bible.

"Then let the burden be on the Knesset to prove that this platform is racist and this candidate is racist," he said. "The orthodoxy will rise up in anger," he added, referring to the country's strictly observant religious Jews, who, while not necessarily backing Kahane, would consider it blasphemous to condemn his platform if it consisted solely of passages from the Bible.

One of the most significant aspects of the Kahane trend, political scientists say, is Kahane's appeal to Israel's youth, particularly among the growing majority of young Jews whose origins are in Arab countries and who are on the lower rungs of the economic ladder.

In a poll of high school students, commissioned by the Van Leer Jerusalem Foundation, 11 percent of the respondents said they would vote for Kahane, and 42 percent said they supported Kahane's ideas, even if they might vote for the Likud Party or a rightist ally. In religious schools, Kahane's support stood at 60 percent, and young Jews from families with origins in Arab countries gave him 50 percent support.

The Van Leer foundation, a generally liberal study institute funded by the Van Leer Group Foundation in the Netherlands, was granted special status by the Knesset in 1958 as an independent, nonpolitical organization. It studies social problems and, according to its prospectus, "moral problems arising from advances in knowledge" and has a reputation here for avoiding involvement with political causes.

The sample of 600 students was scientifically selected, foundation officials said, and the results of the poll were supported by informal opinion samplings by scores of high school teachers who have participated in foundation seminars all over the country.

The force behind the phenomenon appears to be the Brooklyn-born Kahane's proposal for forcibly deporting nearly 2 million Arabs from Israel and the occupied territories and turning the country into a purely Jewish state.

That platform was widely dismissed by most Israelis just a year ago as the rantings of an unbalanced zealot. But as a result of Kahane's election to parliament, it now is accepted by a growing segment of the population as at least falling within the range of legitimate debate in the public forum and in parliament -- despite the clear opposition to it there.

Nonetheless, Kahane's backing, while growing, still is limited, and it provokes vociferous opposition. Twice this month -- in Tel Aviv and in Jerusalem -- he was prevented from speaking by angry Israelis calling him a fascist.

When he arrived in the United States on Aug. 15 for a month-long visit, 12 major American Jewish organizations issued a statement declaring that "Kahane is not representative of the Israelis, is not representative of American Jewry, and more fundamentally, his words and actions are alien to Judaism."

The statement said that "to confuse this still-isolated virus with an epidemic threatening Israel's vibrant democracy is to misconstrue the phenomenon and exaggerate its threat far beyond its troubling but limited dimension."

"Kahane's election has given legitimization to views that a lot of people may have held but were afraid to express," Alouph Hareven, associate director of the Van Leer foundation, said. "Kahane himself is a self-limiting disease, and in a way is not important. The racist attitudes he symbolizes are far more important."

Kahane, who immigrated to Israel 14 years ago after founding the militant -- and often violent -- Jewish Defense League in the United States, has been arrested numerous times for inciting race violence. In 1980 he was ordered held in administrative detention for six months for allegedly conspiring to place explosives in mosques throughout the West Bank.

His weekly newspaper column, "Rabbi Kahane Speaks," published in The Jewish Press, is laced with unabashedly hateful invective, in which he urges measures of "counterterror" against Arabs with the admonition, "In this deadly war, there are no rules of gentlemanly ethics."

But in a long conversation with Kahane, his measured recitation of the message he tries to get across to Israeli youth in almost nightly rallies provides a deeper insight into the causes of his growing popularity.

"The real danger to Israel doesn't lie in the PLO killing Jews," Kahane said. "The real danger is the Arabs who sit quietly in this country and are good citizens and who will never hurt anybody. They will become a majority and then you have the threat of a Jewish state going under Arab votes."

Kahane argued that Zionism came into being to create a Jewish state. But, citing what he called the "demographic facts of life," he estimated that in 20 years the Knesset will be one-third Arab, and that eventually, given the higher Arab birthrate, Arabs will become a majority in Israel.

"The question is, do the Arabs have a right to have a majority in this country?" he said. "If you answer that, 'Yes, they have a right to have a majority,' then you are anti-Zionist. If you say 'No,' then you are Kahane. It may be painful, but Zionism is antidemocratic, that's a fact."

Israel, he said, was declared in its own constitution to be a Jewish state. That the constitution also guarantees equal rights for all citizens regardless of their religion, Kahane argued, is hypocritical.

He added, "Anyone who believes that an Arab, in a state that is defined legally as a Jewish state, which has a Law of Return that applies to Jews only, whose national anthem speaks of the soul of a Jew yearning, whose independence day celebrates the Arab defeat -- anyone who believes that in view of all these things an Arab living in this country can feel empathy for Israel really has contempt for the Arab."

If his party gains power, Kahane said, he would allow Arabs to stay, with the status of "noncitizens" with personal rights but no voting rights. Palestinians who willingly leave would be paid compensation for their property, he said. Those who refuse to leave, "We'll put on trucks and truck out."

Kahane said he tries to project the image of being "crazy."

"That's an image I really foster," he said. "I'm not a Nazi and I'm not crazy, but I sincerely hope that the Arabs think that I'm a Nazi and crazy. That's the only way we'll be able to guarantee a minimum of bloodshed."

The question of why such a radical ideology is being embraced by a growing segment of Israeli youth has fascinated social and political scientists, and an array of sociological explanations has been offered.

Hareven argues that the affected youth were all born since the 1967 war and grew up with a perception of a double standard: democracy for 4.5 million Israelis and undemocratic military rule for 1.25 million Arabs in the occupied territories.

Young Israelis, Hareven argues, became comfortable with that double image and as a result are more susceptible to embracing an even more undemocratic solution to the "Arab problem" -- forced expulsion -- than are the older generation, which may have viewed military rule over Arabs as provisional.

In interviews, however, young Israelis offered less complex explanations for their attraction to Kahane.

They talked about a recent outbreak of terror against Jews in Israel and the West Bank and about the government's lack of resolve in stemming Arab violence. That lack of resolve, they said, reached its peak with Israel's decision last May to exchange 1,150 Arab prisoners -- many of them convicted terrorist murderers -- for three Israeli soldiers held captive.

They said they were more afraid of Arabs now than before the war in Lebanon, where Shiite Moslem guerrillas and suicide car-bomb attacks on Israeli soldiers imparted in them a new wariness of the Arab enemy.

But mostly they talked about their fears that an Arab population explosion eventually would swamp Jewish Israel and achieve through the ballot box what the bullet could not achieve.

Although demographers say the Arab population in Israel and the occupied territories should rise to only 40 percent by the year 2000 and that Israel will retain its Jewish dominance even longer if it returns to the pre-1967 borders, Kahane's supporters seem unconvinced.

"Rabbi Kahane represents a straightening of the path," said David Braverman, a construction engineer who immigrated here two years ago from Los Angeles. "There's one Jewish state and 26 Arab states, and frankly this is just an exchange of populations."

Braverman added, "I didn't bring my children here to live in an Arab state and live in fear."

"Every attack on Jews, every explosion, every murder gives us more seats," Kahane said. "It's a sad thing that we have to learn from such tragedies, but we do."

As Kahane spoke in the Yemenite Quarter's playground, Warked Mahmoud, 41, an Arab waiter from a nearby restaurant, listened quietly in the midst of the Jewish audience.

"I don't have anything to fear. I'm an honest man. I've been working with Jews since 1958, and I've never had an unpleasant incident. But it hurts me to see these youngsters going after a man like this who's crazy," Mahmoud said, shaking his head.

"Everyone I talk to now -- they live in the neighborhood and I know them all -- when they see me, they say, 'Maybe we shouldn't throw them all out.' But when I leave, they go back to saying all Arabs should get out," Mahmoud said. "So, you see, maybe it isn't that serious. Maybe."