LEIPZIG, GERMANY -- They have names like Hitler Youth Schoenefeld, the Fascist Storm Youth, the Rautnitzer Rightists. They are young boys and girls of 17, 15 and 13.

On weekend evenings, they chant "Heil Hitler" and smash storefront windows along the same boulevards where tens of thousands of Leipzigers walked by candlelight a little more than a year ago, silently pressing the case for more democracy in rigidly run Communist East Germany.

In this city where East Germany's peaceful revolution began, young people are challenging the shrinking police force, rioting at soccer games and using a mix of Nazi slogans and street crime to rebel against the new society.

Leipzig is not alone. Neo-Nazi and skinhead groups also have taken to the streets of eastern Berlin and Chemnitz. Berlin was rocked in mid-November by hand-to-hand combat between police and more than 1,000 youths -- some of them squatters but many of them from west Berlin's anarchist scene -- who had occupied empty apartment buildings in the eastern part of the city.

The German Constitutional Protection Office, which monitors extremist groups, estimates that there are about 30,000 neo-Nazis in eastern Germany, about the same number as in the west.

The outbreak of street violence in the first months after German unification has sent a shock wave across a country where many had been marveling at how smoothly the historic transition had been going. Plans for a final east-west soccer game last week were canceled because of fears of violent hooliganism. On Nov. 3, Leipzig police shot and killed a soccer hooligan.

Those who have studied the surge of violence argue that it is not an expression of political extremism so much as a cry for attention by east German youths who, freed from the tight structure of Communist society, are lost in the relative insecurity of Western life.

Every child who grew up in the former East Germany spent not only school hours but also many afternoons, evenings and weekends under the close watch of the Free German Youth. The East German Communist Party decided school and career paths, and any anti-social adolescent expressions were quickly and efficiently suppressed or punished. Youth workers say that for any youngster who grew up under such conditions, the sudden switch to the vagaries of a market economy can be terrifying.

"In our newly discovered freedom, we've also imported a lot of violence," said Markus Zimmermann, a 25-year-old east Berlin councilman who is in charge of the city's youth programs. "Homelessness, drugs, youth gangs and hatred of foreigners were always here, but with unification, they are actually being expressed for the first time."

Zimmermann and several German sociologists say the violence has been building for years and only now has been allowed to flourish.

"It is very difficult for youth to suddenly be without leadership," Zimmermann said. "An East German was always led, from childhood through education to work and party activities. Now they have to lead themselves. So alcohol consumption is up, violence increases.

"It's a real identity question. What do our souls do with this new freedom?"

"These young people are crying out for recognition," said Jan Peter, the 21-year-old founder and editor of Die Andere Zeitung, eastern Germany's first independent newspaper. The paper has reported extensively on the extremist youth scene.

"They feel like second-class citizens, like they don't belong in this new Western country," Peter said. "Their future is nothing but a hole.

"These are generally not workers' kids. They are mostly kids of teachers, professionals and civil servants. They have a good social background. They are not fascists. They are bad boys and girls who just want to say what people don't like to hear."

According to this view, they get dressed up in black capes and white hoods on weekends largely to have something to do, and preferably something that will upset their elders; they know that any reference to Nazi tactics or slogans will especially frighten the authorities, so they specialize in Hitler salutes and chants.

The surge in violence in eastern Germany coincides with a reduction in the number of police on the street, both to free citizens from the police-state atmosphere of the former Communist government and to save money. More than 1,000 officers have been laid off in Leipzig alone.

But the combination of fewer police and more trouble has increased worries of political disarray. "I'm afraid of polarization like we had in the '20s," Peter said, referring to the period of turmoil in Germany that preceded Adolf Hitler's rise to power. "These militant groups can destabilize the system very easily."

Zimmermann and Berlin police say they suspect that some of the youth gangs are being supplied with weapons and strategy by former employees of East Germany's disbanded Stasi secret police. Earlier this month, Berlin officials found right-wing demonstrators equipped with radio phones and other high-tech communications devices that they suspect came from the Stasi.

Those who have studied the violence are worried about another aspect of the new Germany: the thriving black market in Soviet weapons. Disgruntled and bored Soviet soldiers, whose bases are close to every major east German city, sell everything from pistols to rocket launchers, making the new gangs potentially dangerous.

In the old East Germany, the idea of teenagers rampaging through the streets on a Saturday night was inconceivable. Instead, young people were required to be members of the Free German Youth, a Communist Party-sponsored group that embraced some of the mass demonstration techniques of earlier times, including torchlit parades.

Beginning in eighth grade, all East German students became members of the organization. Earlier, they participated in the Young Pioneers, uniformed child brigades that met in afternoon study sessions and military-style outdoor activities.

"The youth of any country are opposed to the state," Zimmermann said. "But this attitude was not allowed in the Free German Youth. Discussions about the biggest political problems -- the {Berlin} Wall, freedom to travel, why the Communist Party was alone in power -- were strictly forbidden."

The youth organization still exists, but only 30 youths in Berlin still belong, Zimmermann said. A year ago, there were 2 million members.

The government is trying to fill the gap by opening youth clubs, starting a telephone hot line for troubled youths and offering counseling. But youth workers say there are not enough resources.

"No one can change overnight," Zimmermann said, "and that is true for young people, too."