In each attack, a suicide bomber detonated a vehicle packed with explosives and gas canisters near police and civilian targets in crowded areas.
The Iraqi state broadcaster put the toll at at least six people, but the US military has so far confirmed the deaths of only two Iraqi policemen in the second explosion, which occurred in Ameriyah, outside Falluja.
surfdog1958, Baton Rouge, USA
Send us your views"Coalition forces confirmed that the Ameriyah citizens exposed to the chlorine were treated locally for symptoms ranging from minor skin and lung irritation to vomiting," Hollenbeck said in a statement.
Brigadier-General Abdel Karim Khalaf, Iraqi interior ministry operations director, suggested the bombings may have been carried out in response to recent government operations against fighters in Ramadi.
Fighters have modified their targets, adding gas bombs to their arsenal, after Iraqi and US forces recently launched a large-scale operation in and around the capital Baghdad to quell violence.
There have been five "dirty bombings" since January 28 in the western Anbar province, with two similar bomb blasts reported in the capital Baghdad.
The use of chlorine is a relatively new tactic. At best, exposure to the gas causes eye and lung irritation, at worst a victim's lungs dissolve from the inside.
Its use is raising concerns of a style of warfare dating back to world war one when chlorine was used by the Germans. It caused panic among soldiers who were unprepared for gas warfare.
So far, the devices in Iraq have caused widespread fear and a choking sickness, but not mass deaths.
But experts say no sophisticated knowledge is needed to cause havoc with industrial chemical weapons.
Chlorine is easily accessible in Iraq. It is used for water purification plants, bleaches and disinfectants.
Chlorine canisters are loaded on to trucks with bombs. When the device goes off, the container is punctured and the chemical released.
Instructions on making chlorine-based bombs can be found on the internet.