Traditional May Day demonstrations sparked violence in Russia and Germany, where up to 100 people were arrested.
A neo-Nazi march in Leipzig had to be abandoned as police turned water cannons against a group of left-wing protesters who threw fireworks at officers securing the route.
Thousands of leftist demonstrators rallied peacefully before the planned far-right extremist march. But when the 800 neo-Nazis began moving through the streets, a group of the leftists began throwing firecrackers at officers charged with keeping the two sides apart.
Police responded with water cannons and baton charges and 30 leftists were arrested.
In Berlin, police arrested 65 people in clashes with revellers celebrating May Day in the early hours of yesterday. But the authorities said the disturbances had been mild compared with previous years. Police were swamped by demonstrators in the early hours of 1 May 2004, and 50 officers were hurt by flying bottles and stones after a concert in the east of the city.
"Given the amount of damage and the number of police injured, it's clear that there was less trouble than on this night last year - so that the situation could almost be described as peaceful," said a Berlin police spokesman.
In Moscow tens of thousands of Communists, unionists and opposition activists rallied for protests over sweeping social changes mixed with anti-government demonstrations. Police closed many streets in the centre and searched demonstrators.
Communists marched under pictures of Lenin and Stalin and traditional hammer-and-sickle banners, with slogans such as "Rise, Save Russia!".
Radical activists from the National Bolshevik Party and the Red Youth Avant-Garde political group clashed with riot police, erecting improvised metal barricades after several activists were detained by police.
In Paris, far-right leader Jean-Marie Le Pen marked the May Day workers' holiday by urging the French to reject the EU constitution, while thousands used traditional marches to voice job concerns and resentment over the cancellation of the traditional Pentecost bank holiday, which falls on 16 May. "Don't mess with my holiday," said banners held up by members of the CFTC trade union.
Unions said that 100,000 people turned out to march at demonstrations across France, although police put the figure at 72,000. The largest march was organised by the powerful Communist-backed CGT union in Paris, attracting 9,000 people.
M. Le Pen and some 3,000 supporters of his far-right National Front party used the May Day rally to broadcast their anti-immigrant, nationalist message.