The organisation singled out three institutions - the University of Johannesburg (UJ), the Vaal University of Technology (VUT) and the University of Venda (UniVen) - for increasing tuition fees for the upcoming academic year.
Shikwambana said they would not stand for the hike and promised "harsh" action.
He urged universities to comply with the demands or face a rolling shutdown aimed at making them "ungovernable".
He also called on universities to put "serious measures" in place to combat gender-based violence.
"It is high time that we resort to anarchy as the members of the EFF students command if nothing is done. We are going to run all these institutions of higher learning ungovernable if they are not in compliance to our demands (sic)," he said.
"There will be serious anarchy. We know they are going to arrest us and we have a plan for that: there will be bouncers behind us. When police come, bouncers will beat them - so we are ready for them and our bouncers are there."
EFF student command threatens anarchy at SA universities
Image: Google Maps/Screenshot
The EFF student command has threatened to unleash anarchy on South African universities from next week if three of its demands are not met.
It wants all institutions of higher learning to allow walk-in registration, to provide free student registration and to cancel historic student debt.
Failure to meet these demands, warned student command president Mandla Shikwambana would result in "anarchy".
Shikwambana, speaking on Friday at a press conference at the Birchwood Hotel, Ekurhuleni, said EFF "bouncers" - possibly the party's paramilitary known as "defenders of the revolution" - would be ready to confront police.
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The organisation singled out three institutions - the University of Johannesburg (UJ), the Vaal University of Technology (VUT) and the University of Venda (UniVen) - for increasing tuition fees for the upcoming academic year.
Shikwambana said they would not stand for the hike and promised "harsh" action.
He urged universities to comply with the demands or face a rolling shutdown aimed at making them "ungovernable".
He also called on universities to put "serious measures" in place to combat gender-based violence.
"It is high time that we resort to anarchy as the members of the EFF students command if nothing is done. We are going to run all these institutions of higher learning ungovernable if they are not in compliance to our demands (sic)," he said.
"There will be serious anarchy. We know they are going to arrest us and we have a plan for that: there will be bouncers behind us. When police come, bouncers will beat them - so we are ready for them and our bouncers are there."
EFF student command hits back at Julius Malema's comments
Shikwambana said there would also be a march to the offices of the National Student Financial Aid Scheme (NSFAS), which he accused of embezzling funds meant for students in the form of its reported R10.3bn irregular expenditure over the past two years and by "creating ghost students under false pretence".
Sit-ins could also be staged at various government offices. Shikwambana said the student command planned to lead unemployed graduates to them.
He warned that corruption at universities would also be confronted. He said the group was "not going to smile at anything that looks and smells like corruption".
Tshwane University of Technology (TUT) was also singled out for alleged corruption. The student command accused higher education and training minister Blade Nzimande of turning a blind eye to it, claiming that people in the government were benefiting.
Shikwambana said UniVen had spent R58m on a swimming pool that could barely accommodate 20 people at one time. He said he believed that money had been siphoned off in the process.
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