When Algerians filled their country’s streets to demand political change, it looked at first like a familiar story of hopes for democracy bound to turn to despair.

A few weeks earlier, in another corner of the Arabic-speaking world, Sudanese protesters had been met with violent crackdowns and tightening government control. It was typical of rising repression and stalling democracy worldwide.

On Monday, though, Algeria took a different direction. Abdelaziz Bouteflika, the president for 20 years, announced he would not seek a fifth term after all. Instead, a convention would be called to draft a new constitution and oversee a peaceful transition of power.

Algeria’s power brokers, particularly in the military, are all but certain to continue pulling strings from the shadows — indeed, Mr. Bouteflika, 82, is so debilitated by illness that many view him as little more than a figurehead.