Euronews reported the rallies, which followed last week's violent demonstrations, went ahead without police authorization. The Italian news agency ANSA said there were no reports of violence as the students, accompanied by some teachers, marched in Rome, Catania, Florence, Palermo, Pisa and elsewhere.
Some protesters carried self-made shields, but one student told Euronews, "These are not shields to fight in clashes, we're carrying them for effect. They have important messages on them that we'd like to send to everyone here."
Rome police Chief Giuseppe Pecoraro had warned people not to wear helmets during the marches. Some protesters responded Saturday by wearing colanders or bowls on their heads, the Italian news agency AGI reported.
AGI said police looked on impassively, despite verbal abuse by some marchers.
ANSA said the protesters proclaimed they were "fighting for our future." Among the government actions they oppose is a proposal to privatize schools.
"We are protesting against the cuts to the education budget that were carried out by both the Berlusconi and Monti governments," one unidentified demonstrator told Euronews.
Unemployment among young Italians is at 35 percent.
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