BAGHDAD  Commanders of the Multi-National Force-Iraq, as the American-led coalition is formally called, have a looming nomenclature problem.

Two days from now, there will no longer be any other nations with troops in Iraq  no “multi” in the Multi-National Force. As Iraqi forces have increasingly taken the lead, the United States is the last of the “coalition of the willing” that the Bush administration first brought together in 2003.

That is partly because the Iraqi Parliament left suddenly for summer recess without voting to extend an agreement for the British military to keep a residual training force of 100 soldiers in Iraq. As a result, those troops must withdraw to Kuwait by Friday, according to a British diplomat, who declined to be identified in keeping with his government’s practice.

As for the other two small remnants of the coalition, the Romanians and Australians, the Australians will be gone by July 31, too, and the Romanians left last Thursday, according to the Romanian chargé d’affaires, Cristian Voicu. NATO will keep a small training presence in Iraq, but its troops were never considered part of the Multi-National Force because of opposition to the war from many NATO countries.