VETSCHAU, Germany (AP) _ One of Gerda Zerna's most cherished keepsakes is a 1983 snapshot showing her son Mike, holding his baby brother Oliver.

The two boys were always buddies, until Mike's recent murder by a neo-Nazi mob.

Mike was only 22. Extremists bludgeoned him outside an east German bar and then toppled a one-and-a-half-ton van onto his broken body - just because he had long hair.

Gerda Zerna contends most Germans and the authorities don't want to admit the magnitude of the far-right threat.

''Reality is being ignored. The leaders of these (neo-Nazi) groups are loose on the streets, telling younger kids that violence is a good thing,'' said Mrs. Zerna.

In February, Interior Minister Rudolf Seiters claimed that ''state measures ... are working'' against neo-Nazi violence, and many believed him.

Federal authorities point out that attacks against foreigners and other far-right crimes have declined from a peak of 536 last September to a monthly average of about 150 so far this year.

The Interior Ministry attributes the drop to bans on four neo-Nazi organizations, other new anti-extremist measures, and grassroots protests.

But, while far-right crimes have indeed dropped since last fall, the count for the first four months of 1993 has actually outpaced the number for the same period last year: about 600, compared with 472.

That works out to five such crimes a day for the start of this year, about one-fifth of them arson attacks on asylum shelters.

Neo-Nazi crimes appear to be a seasonal phenomenon in Germany, with the greatest surge occurring in summer and autumn. That was the case in 1991 and again last year.

Even if that doesn't happen this year, the final hate-crime tally for 1993 could surpass last year's record 2,285 at the current pace.

There were 17 killings last year and 2,200 injuries. A Turk and two Germans have died so far this year, and 300 people are known to have been injured.

Known membership in extreme-right groups is up, according to the Federal Office for the Protection of the Constitution, which monitors extremists: from about 39,800 in 1991 to 42,700 at the end of last year.

Neo-Nazi organizations have easily circumvented the federal ban by changing their names.

But the government insists it has not been trying to play down the far- right threat. Interior Ministry spokesman Detlev Bouke said the new law enforcement measures have made neo-Nazis more hesitant to attack.

''But that doesn't mean it's time to give the all-clear,'' he said.

No one needs to tell that to families of neo-Nazis' victims.

Mike Zerna lived with his parents and three brothers in Vetschau, a working-class community about 60 miles southeast of Berlin.

He was a ''roadie'' for a heavy-metal band, and was caught in tensions between rightist and leftist extremists on Feb. 26 at a leftist bar in Hoyerswerda, a town that earned notoriety in 1991 when residents cheered a far-right attack on an asylum shelter.

A band of skinheads showed up at the bar the night Zerna's band was playing, and a brawl erupted outside.

According to witnesses, about 20 skinheads kicked Mike with their heavy paratrooper boots and overturned a van onto him.

Mike died in a Hoyerswerda clinic seven days later.

Eight people are in custody for the killing.