After the end of the Polish Campaign, von Greim became commander of the 5th Fliegerkorps which participated in the Battle of Britain.
In the early stages of this battle, von Greim was promoted to General der Flieger.
In 1941, on the Eastern Front, his korps split up and renamed Sonderstab Krim.
In April 1942 he became commander of Luftwaffenkommando Ost in Smolensk, as his korps replaced the 8th Fliegerkorps in the front area there.
In February 1943, von Greim was given command of Luftflotte 6, which continued to support Army Group Centre in its operations.
As part of Operation Citadel, von Greims Luftflotte provided 730 aircraft in July 1943.
Due to high losses, by June 1944 only around 50 aircraft were operational.

In late 1942, his only son, Hubert Greim, a fighter pilot with 11./JG 2 was listed as missing in Tunisia.
He was shot down, but bailed out and spent the remainder of the war in a prison camp in the United States.
After the end of the Polish Campaign, von Greim became commander of the 5th Fliegerkorps which participated in the Battle of Britain. In the early stages of this battle, von Greim was promoted to General der Flieger. In 1941, on the Eastern Front, his korps split up and renamed Sonderstab Krim. In April 1942 he became commander of Luftwaffenkommando Ost in Smolensk, as his korps replaced the 8th Fliegerkorps in the front area there. In February 1943, von Greim was given command of Luftflotte 6, which continued to support Army Group Centre in its operations. As part of Operation Citadel, von Greims Luftflotte provided 730 aircraft in July 1943. Due to high losses, by June 1944 only around 50 aircraft were operational.
In late 1942, his only son, Hubert Greim, a fighter pilot with 11./JG 2 was listed as missing in Tunisia. He was shot down, but bailed out and spent the remainder of the war in a prison camp in the United States.
Robert Ritter von Greim