The incapacitation of Bouteflika, 76, has heightened concerns about the stability of the energy-rich regional military heavyweight as the energy-rich country moves toward presidential elections next April amid a political power struggle.
Bouteflika was flown to Paris Saturday night after suffering what the officials APS news agency termed a minor stroke.
"His condition is not serious at all," said Algerian Prime Minister Abdelmalek Sellal, a close ally of Bouteflika.
But Bouteflika's widely believed to have been in poor health for some time. He's rarely appeared in public in recent years and has repeatedly gone to France and Switzerland for medical treatment.
He's dropped strong hints that he's ready to step aside for next year's election, that's likely to usher in a new era in Algerian politics.
Bouteflika is one of the last of the generation of veterans who won the grueling 1954-62 war of independence against the French and who have ruled over the country of 35 million since.
Bouteflika wants to handpick his successor -- his younger brother and personal physician Said is seen as the leading candidate -- but faces tough opposition from the generals, particularly the Department of Research and Security, the most powerful of the country's intelligence services.
This shadowy cabal known as "le pouvoir" -- the Power -- has long held the reins in what is ostensibly a democracy of 35 million people.
The generals reportedly favor Ahmed Ouyahia, a former prime minister, to succeed Bouteflika.
Ouyahia is head of the National Democratic Party, the junior partner in a longtime coalition with Bouteflika's National Liberation Front, the party that led the country to independence.
Amid what looks like it could be a period of intense political feuding, Algeria is being seen externally as the lynchpin of a regional struggle to contain and crush Islamic militancy.
Al-Qaida of the Islamic Maghreb is waging a spreading regional insurgency centered on war-torn Mali, while at the other end of the Mediterranean jihadist groups are increasingly dominating the war to topple Syrian President Bashar Assad.
But Algeria, the region's military heavyweight which fought a brutal war against its own Islamist rebels in 1992-2002, is increasingly being seen as pivotal power to confront the new Islamist threat, even though the country has no wish to be plunged back into a religious conflict.
In the meantime, Bouteflika is locked in a grim struggle with "le pouvoir," specifically the DRS.
It had gained immense sway, separate from the military, during the Algerian civil war.
Its commander, Gen. Mohamed "Tewfik" Mediene, a member of the Berber minority, became one of the Algeria's most powerful figures.
Bouteflika was elected in April 1999 with the army's support, the first civilian to be president in decades, because the military thought he'd be more malleable than the army officers who'd preceded him.
But with support from the DRS, he followed a more independent path and won considerable popular support.
Bouteflika and Mediene were "widely rumored to have a de facto power-sharing agreement, with neither interfering in the other's affairs," observed the U.S. global security consultancy Stratfor.
In the 2009 election, the DRS backed Bouteflika's request for a third term and approved a constitutional amendment to that effect.
"After Bouteflika's victory, the DRS expected him to help groom a successor of its choosing to run in the 2014 presidential election," Stratfor noted. "But the relationship became strained when Bouteflika started advancing his own succession plan."
Mediene unleashed a furious campaign to undermine Bouteflika and his allies. A major target was the state-owned energy monopoly Sonatrach, the key to the nation's economy and widely seen as a center of official corruption.
Important Bouteflika allies were thrown into prison on corruption charges or hounded out of office.
The power struggle has now essentially become a battle between the DRS and the army, with Mediene elevating members of his long-neglected Berber minority into key positions.
In recent months, the DRS has highlighted new corruption scandals in Sonatrach dating to 2009. These have enraged Algerians increasingly disgruntled with the sluggish economy, unemployment and widespread poverty.
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