BAGHDAD, Nov. 24  The first substantive drawdown of American troops in Iraq has begun, as the first members of a brigade in Diyala Province have started to leave, American military officials in Baghdad said Saturday.

Col. David W. Sutherland of the Third Brigade Combat Team, First Cavalry Division, whose soldiers have been working in Diyala since last November, said all 5,000 of his troops would be gone by mid-December.

However, because of continuing violence in Diyala, another brigade that is already in the country will take the place of the Third Brigade Combat Team.

The replacement soldiers are already in Diyala and are taking over their new jobs, Colonel Sutherland said. The replacement brigade, which had worked in Salahuddin Province, which is to the north and west of Diyala, will leave quieter areas of that province to the Iraqi Army and concerned local citizen groups, said Rear Adm. Gregory Smith, spokesman for the multinational division forces in Baghdad.