Demme was born in Mühlhausen in Thuringia. He entered Army Service (Reserves) on September 15, 1914 as a volunteer in the 1st Recruitment-Depot of the 11th Pioneer Replacement Battalion. During the first years of World War I he served in different units mostly as a pioneer. On August 9, 1917, still as a NCO he became a platoon leader in the 3rd Field Company of the 2nd Pioneer Battalion. From July 15, 1918) to the end of the war Demme served as a platoon leader in 402nd Pioneer Company as Leutnant. When the war was over he retired from the active service on December 21, 1918.
Some 18 years later, on January 5, 1937, Demme reactivated in Reserve Service of the reincarnated German Army but he became an active officer on November 1, 1941 in the rank of the Oberstleutnant. From January 27, 1937 to January 1, 1939, after the infantry training course with the Instruction Infantry regiment Döberitz, he was a Head Trainer for the Condor Legion in Spain. At the same time, as an experienced pioneer officer, he was detached to Selection course with the 43rd Pioneer Battalion. From January 1 to June 8, 1939 he served as an Officer with Special Duties of OKW – Service with the Chief of OKW, Special-Staff W.
In the dawn of World War II Demme was transferred to the Staff of Training Leader Aachen 1 (June 8 – August 26, 1939) and then to the Staff of the Commander of Fortifications at the Lower Rhine until April 10, 1940. In following years Rudolf Demme was a commanding officer in 208th Pioneer Replacement Battalion (April 10, 1940 – July 8, 1941), 92nd Panzer Pioneer Battalion (July 8 – December 15, 1941) and 58th Panzer Pioneer Battalion (December 15, 1941 – October 15, 1942), then he was transferred to Revitalization Staff Centre.
On January 10, 1943 Demme became a Commander the 59th Panzer-Grenadier-Regiment of the 20th Panzer Division and led his unit through the bloody battles on the Eastern front until July 25 1944 (Orel, Brjansk, Mogilew, Witebsk, Newel, Bobruisk, Cholm). He was promoted to Oberst on July 1, 1944. From July 25 to September 20, 1944 he was in Führer’s Reserve and, at the same time, he was detached to the 14th Division Leaders Course, after which he was delegated with the Leadership of the 17th Panzer Division.
In Führer’s Reserve OKH from December 2, 1944 and just few days later he was delegated with the Leadership of the 132nd Infantry Division (December 10, 1944 - March 1, 1945). Demme became a Generalmajor and the Commander of the 132nd Infantry Division on the same day, March 1, 1945, and led his division through the Courland Pocket until the end of the war.