This is from The Oxford Companion to Military History:
Afrika Korps (Deutsches Afrika Korps, or DAK) evolved from ‘Reconnaissance Detachment Rommel’, sent to Tunisia in early 1941. It was expected to have a blocking role, following British defeat of the Italians and the westward advance by O'Connor, and so was strong in machine gun and anti-armour units. Although Hitler gave it the title Afrika Korps on 19 February, it remained small, with 5th Light (later renamed 21st Panzer) and 15th Panzer Divisions. On 15 August 1941, after heavy fighting which had shown that it was the principal Axis combat force in Africa, the Afrika Korps became part of Panzer Group Africa, a title changed on 30 January 1942 to Panzer Army Africa and later to First Italian Army, which became part of Army Group Africa in February 1943.
The Allies tended to call all German troops in theatre, whether part of the DAK or not, the Afrika Korps. And whatever the terminology of the military organization of which it formed part, the Afrika Korps played a consistently distinguished role. At Gazala it hooked round the Eighth Army's desert flank, and although it suffered heavy losses at Alamein that autumn, it fought on resolutely until the surrender in North Africa in May 1943.
There was something about the DAK which commended it to its opponents. It fought hard and skilfully, developed a sartorial style which mingled the utilitarian with the flamboyant, and behaved with magnanimity in victory and dignity in defeat. The distinguished military historian Ronald Lewin, who witnessed the end in Africa, felt his own pride in victory mingled with ‘a sense of compassion, too: this had been a good enemy.