Lieutenant-General Sir Alexander Galloway, KBE, CB, DSO, MC (3 November 1895 – 28 January 1977) was a senior British Army officer. During the Second World War, he was particularly highly regarded as a staff officer and, as such, had an influential role in the outcome of Operation Crusader during the Western Desert Campaign in late 1941. He later commanded the 4th Indian Infantry Division at the Battle of Monte Cassino during the Italian Campaign in early 1944.

Born in Minto, near Hawick, Scotland on 3 November 1895, the son of a Church of Scotland minister, Alexander Galloway was educated at King William's College. On the outbreak of the First World War in August 1914 Galloway volunteered for the British Army and was commissioned as a second lieutenant into the Cameronians (Scottish Rifles) but was then posted on 8 October 1914 to the 1/4th Battalion, King's Own Scottish Borderers, a Territorial Force unit, part of the 156th (Scottish Rifles) Brigade of the 52nd (Lowland) Division. He was promoted to lieutenant in May 1915, and saw action at Gallipoli, in Egypt and Palestine, and on the Western Front. In 1917, he gained a commission in the Regular Army, returned to the Scottish Rifles, and was promoted to captain in July. He was awarded the Military Cross (MC) in 1918.

Remaining in the British Army during the interwar period, Galloway had a number of regimental and staff jobs, serving from 1925 to 1926 as adjutant to the 2nd Battalion, Cameronians. He attended the Staff College, Camberley for a year from January 1928 and graduated in December 1929. His fellow students there included several future general officers such as Richard McCreery, Gerald Templer, John Harding, Gerard Bucknall, William Holmes, Philip Gregson-Ellis, Gordon MacMillan and I. S. O. Playfair. His appointment after graduating was as including appointments as staff captain at HQ Cairo in February 1930 and also as brigade major of the Canal Brigade in Egypt from February 1932. He returned to the Staff College, Camberley in February 1937 July 1938 as an instructor, and several of his fellow instructors would rise to prominence in the war.

Galloway was promoted to major in December 1933 (having previously been made brevet major) and was made brevet lieutenant-colonel in January 1935. His promotion to lieutenant-colonel came on completing his period instructing at the Staff College in 1938.

At the outbreak of the Second World War Galloway was commanding the 1st Battalion The Cameronians. In February 1940 he was selected to command, in the rank of acting brigadier, the new Staff College at Haifa in Palestine. In August he was appointed chief staff officer (BGS – Brigadier-General Staff) to Lieutenant-General Henry Maitland Wilson's HQ British Troops Egypt. Wilson lent Galloway to Richard O'Connor, commander of the Western Desert Force to help in the planning of Operation Compass. His substantive rank was advanced to full colonel in December 1940.

In early 1941, while still Wilson's BGS, Galloway traveled to Greece (with a pause in Crete where, between 19 February and 7 March, he assumed temporary command of forces on the island) where Wilson was to assume command of 'W Force', the Commonwealth Expeditionary force that arrived during March and April. Overwhelmed by superior German forces in the Battle of Greece, the expeditionary force was forced to evacuate the Greek mainland by the end of April and Galloway returned to Cairo to take command of the 23rd Infantry Brigade, which was in the process of reforming. Galloway was appointed a Commander of the Order of the British Empire in July.

Although sent as part of 6th Infantry Division to reinforce Australian I Corps fighting in the Syria-Lebanon Campaign, the brigade saw no action and by September Galloway was back in Cairo to take up the appointment as BGS to Alan Cunningham, the commander of the newly formed Eighth Army. On 23 November, during Operation Crusader, learning that the British armour had been heavily defeated by the tanks of Erwin Rommel's Africa Corps, Cunningham drafted orders to discontinue the offensive and withdraw his forces. Galloway, on his own initiative, delayed issuing the orders and contacted Cairo to suggest that Claude Auchinleck, the Commander-in-Chief Middle East Command, should come forward to review the situation personally. In the meantime, Galloway discussed the situation with Cunningham's two corps commanders and learned that both Willoughby Norrie (XXX Corps) and Reade Godwin-Austen (XIII Corps) felt the offensive should be continued. These views Galloway passed on during the subsequent conference with Auchinleck at Eighth Army HQ. Consequently, Auchinleck ordered Cunningham to continue the offensive. Although Rommel's "dash to the wire", an attempt to sever Eighth Army's lines of supply, caused alarm and confusion in Eighth Army's rear echelon, Rommel's armour was held at the Libyan border with Egypt by the artillery of 4th Indian Infantry Division and then forced to retrace its steps as a result of lack of supply. Eighth Army thus regained the initiative and by January had pushed the Axis forces out of Cyrenaica.

During Crusader on 27 November 1941, Galloway was promoted acting major-general, to become Deputy Chief of the General Staff (DCGS) at GHQ Middle East. He replaced Neil Ritchie, who had assumed command of Eighth Army. In recognition of his efforts in North Africa, Galloway was awarded the Distinguished Service Order and Mentioned in Despatches in December. In his new role Galloway spent some time in the United States selecting equipment for the Eighth Army before returning to London in May 1942 to take up the important role of Director of Staff Duties at the War Office. His rank was upgraded from an acting one to a temporary one in December 1942 and, in July 1943, he was appointed to command 1st Armoured Division which was re-fitting in North Africa having fought through the North Africa campaign since the Battle of Gazala the year before.