It intially consisted of British and American forces only. They were organised into three separate components, one for each landing site; Oran, Algiers and Casablanca. After the surrender of French forces, French units were also added to its order of battle. It eventually consisted of three corps, the American II Corps, British V Corps and French XIX Corps.
After the landings, Anderson's forces rushed east to try and capture the Tunisian shoreline before German forces reached there in large numbers. They failed. After that failure, a period of consolidation was forced upon them. The logistics support for the Army was greatly improved and airfields for its supporting aircraft greatly multiplied. By the time the British 8th Army approached the Tunisian border, following its long pursuit of Rommel's forces after El Alamein, 1st Army was again ready to strike.
Supported by elements of XII Tactical Air Command and RAF No. 242 Group, 1st Army carried the main weight of 18th Army Group's offensive to finish off Axis forces in North Africa. The victory was won by mid-1943 in a surrender that, in numbers captured at least, equalled Stalingrad. Shortly after the surrender, 1st Army disbanded, having served its purpose.