Mohamed Tadjadit, nicknamed the "Hirak poet", and Noureddine Khimoud were arrested on August 23 and held in preventive detention for "inciting an unarmed gathering" and publishing material that "could harm national unity", according to their lawyers.
Five days later, they began a hunger strike "because they consider that the detention is abusive and unfounded", one of the defence attorneys, Zoubida Assoul, told AFP.
Tadjadit defied a ban on public protests imposed by the authorities in March, at the onset of the novel coronavirus pandemic, and took part in an anti-government rally on August 21 in Algiers, according to local media.
He had been arrested in November last year and sentenced the following month to 18 months in jail on charges of "undermining the national interest".
Tadjadit was among more than 70 members of the Hirak movement who were released from jail in January.
Anti-government protests led by the Hirak movement last year swept ailing president Abdelaziz Bouteflika from power but continued afterwards, demanding the ouster of the entire state apparatus, reviled by many Algerians as inept and corrupt.
Weekly demonstrations rocked Algeria for more than a year and only came to a halt in March due to the coronavirus crisis.
But authorities have in recent months stepped up a crackdown on government critics, including journalists, opposition politicians and Hirak members.
Last month journalist Khaled Drareni received a three-year prison term in a trial rights groups have described as a test of press freedom in Algeria, which was rocked by anti-government protests in 2019 and early 2020.
"It's a very heavy verdict for Khaled Drareni. We are surprised, the case is hollow," lawyer and president of the Algerian League for Human Rights Nouredine Benissad told AFP at the time.
Drareni, 40, editor of the Casbah Tribune news site and correspondent for French-language channel TV5 Monde, was arrested on March 29 on charges of "inciting an unarmed gathering" and "endangering national unity" after covering demonstrations by the "Hirak" protest movement.