In Berlin, where 9,000 police are on alert for the expected protests, there have already been violent incidents.
About 500 protesters in an eastern district of Berlin erected barricades, started fires and threw rocks and bottles at police, who responded with water cannon.
CNN's Bettina Luscher said police and rioters clashed in two separate incidents in the east of the city. She said in one a crowd of 6,000 people confronted police. At least 40 people were arrested and several police officers were injured.
London preparations up
In London, police are mounting a massive security operation involving 6,000 officers in an attempt to avert a repeat of riots that broke out in previous years.
Lord Harris, chairman of London's Metropolitan Police Authority, had warned police might use rubber bullets for the first time on the British mainland if rioters ran amok, although that claim was later dismissed by London Police Chief John Stevens.
Russians join rallies An estimated 300,000 people joined rallies in Russia, many carrying Soviet-era relics such as red flags and portraits of Stalin.
In Moscow, the turnout for two rallies was estimated at about 28,000 -- a shadow of the 150,000-strong crowds that jammed Red Square when May Day was one of the most important dates on the Soviet ceremonial calendar.
