* No sign of veteran president's bid so far
* Bouteflika, 82, has been in Switzerland for medical care
Tens of thousands of protesters rallied in cities around Algeria on Sunday to demand President Abdelaziz Bouteflika step down just as he was due to declare his bid for a fifth term in April elections, witnesses and residents said.
Protest numbers were fast approaching the levels of Friday when demonstrators filled the centre of the capital Algiers alone, in one of the biggest outpourings of dissent - rare in Algeria - since the 2011 Arab Spring uprisings.
Bouteflika, 82, in shaky health for years, was due to submit his official election papers at the Constitutional Council in Algiers on Sunday, the deadline for candidates.
He did not have to do so in person, the state news agency APS said. Bouteflika, rarely seen in public since he suffered a stroke in 2013, was at the weekend still in Switzerland for unspecified medical checks, according to Swiss media.
Opponents of Bouteflika say is no longer fit to lead, citing his poor health and what they call chronic corruption and a lack of economic reforms to tackle high unemployment that exceeds 25 percent among people under the age of 30.
Analysts say the protesters, who began hitting the streets 10 days ago, lack leadership and organisation in a country still dominated by veterans, like Bouteflika, of the 1954-62 independence war against France.
But traditionally weak and divided opposition and civic groups have called for protests to go on should Bouteflika, in power for 20 years, confirm his pursuit of re-election.
The government has played on fears among many Algerians of a return of bloodshed seen in the 1990s when an estimated 200,000 people were killed after Islamists took up arms when the military cancelled elections they were poised to win.
But the new series of protests have been generally peaceful, apart from Friday when scuffles with police left 183 injured.
Thousands of students gathered on Sunday at university faculties, one of them near the Constitutional Council where presidential candidates filed their papers, chanting: "No to a fifth term!" or "A free and democratic Algeria!"
There was heavy security around the Constitutional Council, and police prevented restive students from leaving the campus nearby, keeping the main gates shut.
But thousands were later marching through the centre like on Friday. A diplomatic source estimated as many as 70,000 people had massed in Algiers, including a rally at Bab Ezzouar university, the country's biggest.
"We will not stop until we get rid of this system," said Aicha, a 23-year-old student.
According to witnesses and local television footage, protesters also turned out in their thousands in other cities around the North African country, such as Oran, Constantine, Annaba, Batna, Blida, Skikda and Bouira.
The first candidate to submit his papers was Ali Ghediri, a retired general who is challenging the elite made up of military, ruling FLN party and business leaders. "I tell the people a new dawn has started," he told reporters.
By midday, six candidates had formally registered. There was no sign of Bouteflika's bid. The main Islamist party said in a statement it would boycott the vote if Bouteflika ran again.
Bouteflika changed his campaign manager on Saturday, state media said. He has not addressed the protests against him - the largest since 2011 when popular revolts ousted long entrenched elites in a number of Arab countries, though not in Algeria.
Many Algerians eschewed public political activity for years, for fear of trouble from the pervasive security services or out of disillusionment with the lack of change in the leadership.
After the decade-long Islamist insurgency that Bouteflika crushed early in his rule, Algerians generally tolerated a political system leaving little room for dissent as a price to pay for relative peace and stability.
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