7 September 2013 Last updated at 14:26 ET 
More than 100 demonstrators interrupted the traditional Seventh of September military parade in the city of Rio de Janeiro, shouting slogans against the authorities.
They clashed with police, who threw tear gas and made several arrests.
There were clashes in Brasilia, where President Dilma Rousseff gave a speech.
In Brazil’s largest city, Sao Paulo, hundreds of people have been taking part in a march, which has been largely peaceful.
Activists used social media to call for protests in more than 150 cities.
Brazil saw a big wave of protests in June, as the country prepared to host the football Confederations Cup.
Initially, demonstrators demanded that a hike in bus and underground fares be revoked.
But the demonstrations grew into a much larger movement against corruption and excessive spending in preparations for next year’s World Cup and the 2016 Olympics, which Rio will host.
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Protests at Brazil Independence Day
