One blast hit a car park across the street from Yarmuk hospital in the west of the Iraqi capital, killing at least four people and wounding 10.
The second struck a residential area in Mahmudiyah, south of Baghdad, killing at least four people and wounding at least 13.
Bombings and shootings in the capital were once a daily occurrence, but have declined since the Islamic State jihadist group spearheaded a sweeping offensive last June and overran large areas north and west of the city.
Iraqi security forces and allied paramilitaries have regained significant territory from IS in recent months, with backing from a US-led coalition carrying out air strikes and training, as well as from Iran.
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But large parts of two provinces -- Nineveh in the north and Anbar in the west -- remain under IS control.
Seven people were killed and 31 wounded in a car bomb blast in Baghdad's western neighbourhood of Bayaa yesterday, a police colonel said.
Another two people were killed the same day by a roadside bomb in Taji, just north of the capital, he said.