A video purportedly of the kidnapped children has been released on social media via men who call themselves Amba boys, a reference to the state of Ambazonia that armed separatists are trying to establish in Cameroon's north-west and south-west regions.
They told Africanews, the abductors damaged school property and beat other children before committing the crime.
Cameroon, an English-speaking central African country, has been marred by a separatist rebellion in recent years, the BBC reports.
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The boys also said they were taken by the armed men late Sunday and didn't know where they were being held.
While such mass kidnappings were previously unknown in Cameroon, the abduction came after two major such incidents in neighbouring Nigeria, where the Islamist group Boko Haram snatched more than 200 schoolgirls from the Borno state town of Chibok in April 2014.
A six-minute video seen by AFP, but which could not be immediately confirmed independently, showed 11 boys apparently aged about 15 giving their identity and name of the school in English, and adding that they were abducted by the "Amba Boys" - the name for anglophone separatists.
Forty-eight hours after the abduction of 79 children from a local school in Bamenda, capital of Cameroon's restive North West region, parents have been flooding the campus for any available information on their children. All they want is for us to close the schools.
"We shall only release you after the struggle".
How did the Anglophone crisis begin?
Fighting between the military and separatists increased after the government clamped down on peaceful demonstrations by English-speaking teachers and lawyers protesting what they said were their marginalisation by Cameroon's French- speaking majority. Many Anglophones have long complained that their regions were being neglected and excluded from power since a referendum vote in 1972 saw Cameroon dropping its federal form to become a unitary state.
Most of Cameroon is French-speaking, while the country's western portion is populated by English speakers.
The turmoil in Cameroon comes as President Paul Biya, who has led since 1982, easily won a seventh term last month in an election that the United States says was marked by irregularities.
Opposition parties allege that the poll was rigged, but legal attempts to overturn the result failed.