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The BBC's Yusuf Yakasai in the city says there is pandemonium with people running all over the place and plumes of smoke rising into the sky.
One of the blasts hit the federal police headquarters in the city and two other police stations, he says.
No-one has claimed responsibility for the attacks, but Islamist militants have been behind a recent campaign of violence in the mainly Muslim north.
Our reporter says there is also a shoot-out going on at the police's state head office in the east of the city.
The blasts targeted different neighbourhoods of the city.
So far he is aware of explosions at the federal police headquarters in the west of the city, one police station in the centre, and another police station in the south.