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8 year oldThe new law would allow the authorities to tap phones, snoop on email and deploy hidden cameras and bugs.
It would help Switzerland catch up with other countries, supporters say.
Opponents have feared it could erode civil liberties and put Swiss neutrality at risk by requiring closer co-operation with foreign intelligence agencies.
Some 65.5% of voters agreed to accept the proposal. It will allow the Federal Intelligence Service and other agencies to put suspects under electronic surveillance if authorised by a court, the defence ministry and the cabinet.
The big vote in favour of new powers for the intelligence services shows just how concerned the Swiss have become about a possible militant attack.
For decades, ever since a scandal in the 1980s in which Switzerland's government was revealed to have been spying on tens of thousands of its citizens, the Swiss have been sceptical about state surveillance. CCTV cameras are rare; even Google Street View is restricted because of Swiss privacy laws.
But the dreadful events in neighbouring France have changed many Swiss minds. Despite arguments from opponents that increased surveillance would not automatically increase security, voters handed huge new powers to their intelligence services.
The Swiss government says the powers would be used about once a month to monitor the highest-risk suspects.
The new law was not comparable to the spying capabilities of the US or other major powers, which "go well beyond what is desired in terms of individual liberty and security for our citizens", Defence Minister Guy Parmelin said earlier this year.
Swiss law currently prevents authorities from relying on anything more than publicly available information or tips from foreign officials when monitoring domestic threats, according to a government website.
The new surveillance law was passed last year but has not yet been enacted after opponents collected enough signatures to force a referendum under Switzerland's system of direct democracy.
On Sunday, Swiss voters also rejected a proposal to boost state pensions by 10% - an initiative supported by the left but considered too costly by opponents. Voters also rejected another initiative to reduce Switzerland's ecological footprint.
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