In three decades in office, Mr. Bashir proved ruinous for his country and people, and his exit is another testament to the power of mass protests against tyranny. In company with a similar uprising in Algeria, which led to the removal of its long-serving despot last week, it shows that the yearning for greater freedom remains strong in the Arab world, despite the failures of the Arab Spring.

To be sure, Sudan faces immense obstacles to overcome the damage Mr. Bashir wrought. Among many other offenses, the ousted dictator was indicted by the International Criminal Court on war crimes charges for the mass killing of civilians in the Darfur region a decade ago. Mr. Ibn Auf, who announced he will lead a two-year transitional government, is himself under U.S. sanctions for his role in Darfur. He is part of the kleptocratic regime that looted Sudan and is manifestly unfit to lead a transition.

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Sudan needs a clean break with the past and a credible transitional government that can appeal for international economic aid, as well as construct an open and pluralistic system. Mr. Ibn Auf is not that leader, and the transition need not take the two years he announced. If he is to avoid more popular unrest, he should appoint civilians to lead the transition; the Sudanese Professionals Association, which spearheaded the revolt, could provide new leaders. The group denounced Mr. Ibn Auf’s decision to head an interim regime, saying it was “a coup to reproduce the faces and institutions that our great people revolted against.”

Mr. Bashir’s whereabouts are unknown. If Sudan is to surmount its past, he must be held to account for his crimes, either at the ICC or at home, along with all those in his bloated military and intelligence services who aided and abetted them.

Despots like Mr. Bashir often assume they can survive no matter what people on the street think. Such despots should pay close attention to what happened in Sudan, where protests began against economic misery and were fueled by resentment of corruption, arrogance and indifference by Mr. Bashir and his cronies.

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President Trump ought to take a lesson, too. What has happened in Algeria and Sudan shows that his administration’s blind backing of other Arab autocrats, including Abdel Fatah al-Sissi of Egypt and Mohammed bin Salman of Saudi Arabia, is a bad bet.