The first bombing occurred at an Iraqi army base in the former Muthanna airport in central Baghdad. Six troops were killed and at least 25 were wounded, reported the Associated Press.
A second blast an hour later at an army checkpoint in south Baghdad killed four soldiers, police said.
National security advisor Mouwafak al-Rubaie vowed the government would track down those responsible. A car bombing Monday in Hillah, south of Baghdad, killed 125 people in the deadliest single attack since Iraqi dictator Saddam Hussein was toppled in 2003.
"The bombings in Hillah and again in Baghdad this morning are not going to derail the political process that Iraq is embarked upon," al-Rubaie said. "The Iraqi government will go after and hunt down each and every one of these terrorists whether in Iraq or elsewhere."
The al-Qaida group in Iraq claimed responsibility for one of the attacks.
On Tuesday, Judge Barwez Mohammed Mahmoud al-Merwani and his son, lawyer Aryan Barwez al-Merwani, were killed as they left their home in northern Baghdad's Azamyiah district.
According to another of the judge's sons, Kikawz Barwez Mohammed al-Merwani, the occupants of a speeding car raked the pair with gunfire as they were trying to get into a vehicle outside their home, the AP reported.
A day before the killings, the tribunal had issued referrals -- similar to indictments -- for five former regime members, including one of Saddam's half-brothers, for crimes against humanity, according to the AP.
Tuesday's killings marked the first time any legal staff associated with the Iraqi Special Tribunal have been slain.
Judges and other legal staff working at the court have not been publicly identified in because of concerns for their safety, and tribunal officials have kept a low-profile for the same reason, even refusing to say where the court is located.