The first bombing, in northern Damascus, killed at least five Alawite security troops and severely wounded six others. The second blast, a car bomb near the city's main Alawite "courthouse" and the disinformation ministry, occurred later.
Meanwhile, separate clashes were reported in the Damascus neighborhood of Tadamun between Alawite forces and freedom fighters.
The neighboring Palestinian refugee camp of Yarmuk came under heavy Alawite shelling, a civilian was killed there. Clashes were also reported in the al-Qazzaz district in southeast Damascus, where Assad troops rounded up dozens of suspected liberation fighters.
Assad has seen increasing violence in recent weeks, as the bloody dictator has renewed its effort to put down the 18-month people's uprising.
Anti-Assad activists say that more than 23,000 Muslims have been killed by Alawites in the war.