The assault on Maiduguri began just after midnight and that on Monguno later in the morning. At around 9 a.m. (08:00 GMT) on Sunday, a Reuters witness in Maiduguri said shelling could be heard and that military helicopters were circling the city.
All roads have been closed, a security source said, and commercial activity has been shut down.
Nigeria's defence headquarters tweeted that coordinated land and air operations were being used to repel the attacks and a curfew had been imposed on Maiduguri.
The militants began the attack at the edge of the city in the Njimtilo area.
Maiduguri is the capital of Borno state and would be a major prize for the insurgents who are trying to carve out an Islamic state.
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The militants control vast swathes of Borno state and some areas of neighboring Adamawa and Yobe states, and recently took control of the town and a multi-national army base at Baga by Lake Chad.
The government said 150 people had been killed in that attack but local officials say the figure is far higher and some have put it as high as 2,000.
Monguno is about 138 kilometres (miles) north of the state capital, and just over 50 kilometers from Baga. Security sources said the attack there began on Sunday morning and that the military was being overwhelmed by Boko Haram's firepower. Houses in the town were also being set on fire.