In recent weeks, Europe's justice commissioner has pledged that Europeans' rights would not be sacrificed for U.S. national security.
The student group also seeks more clarity from the tech companies on how they handle users' personal data under European procedures.
Facebook, Apple, Microsoft, Skype and Yahoo could not be immediately reached to comment on the complaints.
In 2006, E.U. data protection authorities already decided in a case involving the payment processor Swift that a mass transfer of data to the U.S. authorities is illegal under EU law, the student group said.
Google and YouTube were not included in the first round of complaints, the group said, because they do not use European intermediaries.
"But since Google has data centers in Ireland, Belgium and Finland, we can take similar actions on a slightly different path," they said.
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