In addition to the formations from the United Kingdom and British Commonwealth, formations from other nations fought in the Western Desert campaign from December 1940 until November 1942. These included:

The Polish Carpathian Brigade,
Free French Forces
Greek Forces

The Polish Carpathian Brigade began its existence as part of the French Army of the Levant (Syria and Lebanon), being formed on 12 April 1940. About three-thousand, five-hundred men came together who had escaped from Poland through Romania and into Turkey to form two regiments of infantry, one horsed cavalry regiment, with some artillery and supporting arms and services. The French Army parented the new brigade as prior to the fall of France, the U.K. and France had an agreement that the U.K. would host escaped Polish naval units while the French hosted army units. Major General S. KOPANSKI commanded the brigade, as in the Polish Army the rank an officer held was linked to their seniority rather than the appointment they held.

On 20 June 1940, the brigade came under command of the British G.H.Q. Middle East Command following the fall of France, and the brigade moved to Palestine at the French Levant sided with the Vichy Regime set up in France. The brigade remained part of the Polish Army, reporting to the Polish Government in Exile established in London, but came under operational command of the British Army. On or about 2 October 1940, the brigade moved to Egypt, as Italy had declared war on the U.K. to be deployed around Alexandria. In August 1941, the Commander-in-Chief ordered the brigade to move to Tobruk to relieve the 18 Australian Infantry Brigade in the fortress that was surrounded by the Axis forces. The troops arrived in Tobruk on 21 August 1941 on board warships used to supply the isolated garrison.

The units of the brigade saw action in the defence of Tobruk and participated in the battle of Gazala that resulted in the relief of Tobruk. For a time, the brigade came under command of XIII Corps from 11 December 1941 until 3 February 1942, and then the 1 (South African) Infantry Division from 3 February 1942 until 15 March 1942. By this date, STALIN had released a large number of detained Polish Army personnel and their dependents, who moved through the Caucasus mountains to Iraq and then consolidated in Palestine. The Polish Carpathian Brigade moved to Palestine to be integrated into the new Polish Army in the East as a brigade in the new 3 Carpathian Infantry Division. As such, it later served in Italy in 1944 and 1945, but never returned to its native land.