The second and final term of President Joseph Kabila expired on Monday night.
His critics say he's flirting with disaster if he attempts to hold onto power indefinitely.
Armed police have set up checkpoints around the capital, Kinshasa.
Soldiers are in position across the sprawling capital of 12 million people.
Opposition politicians speak of a "trial of strength on the streets" in coming days.
Is that a recipe for renewed turmoil?
Presenter: Martine Dennis
Kikaya Bin Karubi: Adviser to President Joseph Kabila
Ida Sawyer: Human Rights Watch
Source: Al Jazeera News