One of the blasts blew a large hole in the six-story main government building that houses the headquarters of Prime Minister Abdelaziz Belkhadem. That explosion is believed to have been caused by a suicide car bomber.
Belkhadem was unhurt. He called the attack a "cowardly, criminal terrorist act."
The second explosion at a police station in the city's eastern outskirts.
Dgouher, a resident of Algiers, spoke to RFE/RL today shortly after the blasts. "It's total chaos," he said. "[Telephone] networks were down. We can't contact our relatives and friends. It's panic. Everything is closed. People are stressed and frightened. There are screams everywhere, people running, trying to find their families. It's chaos."
Al-Jazeera television reported that a group known as the Al-Qaeda Organization in the Islamic Maghreb claimed responsibility for the bombings.
Formerly known as the Salafist Group for Preaching and Combat (GSPC), the faction has deepened its ties to the Al-Qaeda network, and has taken responsibility for a number of deadly attacks on security forces and foreigners in Algeria since January.
(compiled from agency reports)