One report says the security forces have used tear gas, but the scale of the trouble is not yet clear.
Tens of thousands of people have arrived in Genoa to demonstrate against what they see as the adverse effects of globalisation on poorer countries.
Behind four-metre high steel barriers sealing off the old city, the G8 presidents and prime ministers will discuss the potential for a world recession, liberalising international trade, and efforts to combat global warning.
And in an effort to make the summit look less like a "rich man's club", the group has invited representatives of developing countries to join them on Friday evening, when they plan to announce a $1bn global health fund to fight Aids, TB and malaria.
The BBC diplomatic correspondent Barnaby Mason, who is in Genoa, says this is unlikely to appease campaigners, who want more concrete action to write off the debts of the poorest countries.
The more militant demonstrators, led by Italy's Tute Bianche - the White Overalls - have vowed to breach the summit's security perimeter and get into the secure "red zone".
Armoured vehicles, water cannon and ranks of mounted police officers have been drafted in to try to ensure this does not happen.
The Genoa Social Forum, an umbrella group for about 700 protest groups, has been giving protesters lessons in self-defence ahead of expected clashes with the security forces.
Click here to see the extent of the red zone and the outer security perimeter (the "yellow" zone)
Inside the meeting, the G8 leaders are expected to endorse calls for a new round of world trade talks, and offer concessions to developing countries, many of whom have been reluctant to take part.
But the meeting is unlikely to resolve the serious differences between the United States, Europe and Japan on the scope and purpose of the trade negotiations, which have been stalled since December l999.
The summit, which is being held in the city's Palazzo Ducale, will also discuss the problems of the world economy, which is slowing down dramatically.
The US is expected to press European leaders to do more to stimulate their own economies, including urging the European Central Bank to cut European interest rates further.
The political leaders say they want to deepen dialogue with their citizens, including peaceful protesters, but they condemn violence and say they will not allow it to prevent meetings like the G8 going ahead.
US President George W Bush has gone further, attacking what he described as the "isolationism and protectionism" of anti-globalisation demonstrators.
Speaking as he set off from the UK to attend the conference, he told them: "You embrace policies that lock poor people into poverty. Trade has been the best avenue for economic growth for all countries."
Our correspondent says the protesters themselves are divided on tactics.
Some activists are describing the Genoa protests as the most ambitious so far. Peaceful campaigners say the violent few are grabbing the spotlight and diverting attention from serious arguments.
Recession in Japan and a sharp slowdown in the United States are spreading to Europe, threatening global trade and growth.
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