The first explosion occurred at around 8:30 pm (1730 GMT) in the Iskan neighbourhood near a group of civilians, an AFP journalist at the scene and an interior ministry official said.
The second blast came as emergency services arrived at the scene to treat the wounded.
The ministry official put the toll at nine dead and 21 wounded, while a defence ministry official said nine people were killed and 25 injured. Both said security forces members were among the casualties, but gave no specifics.
Both officials also spoke on condition of anonymity.
Three other attacks in the capital left a dozen people wounded in total, the interior ministry official said.
Meanwhile in the main northern city of Mosul, two Iraqi soldiers were shot dead by gunmen using silenced pistols, according to a police officer who did not want to be identified.
And just south of the restive central city of Baquba, in Diyala province north of Baghdad, a woman was killed and her husband was wounded when gunmen stormed into their home and opened fire, police said.
Despite a decline in violence since its peak in 2006 and 2007, attacks are still common nationwide. A total of 185 Iraqis were killed in violence in September, according to official figures.
Copyright AFP (Agence France-Presse), 2011