For game purposes the ELAS and EAM partisans can operate together, while the EDES partisans must operate alone or with British support. Any of the partisans can use any unit or formation designated for the "Resistance" or for their affiliated group.*
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There were three major partisan groups, and several smaller ones, operating in Greece during World War II.  Their affiliations and ideologies ran the spectrum from one end to the other. There were communist, royalist, fascist and democratic para-military groups operating in Greece at one time or another during this period.  The principle groups were:*
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Ethniko Apeleftherotiko Metopo (EAM), in English: National Liberation Front. *
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Ethnikos Laikos Apeleftherotikos Stratos (ELAS), in English: Greek People's Army of Liberation. *
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Ellinikos Dimokratikos Ethnikos Stratos (EDES), in English: National Greek Democratic League or National Republican Greek League. *
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The EAM and ELAS were considered left-wing groups, while the EDES was considered right-wing. Such general labels do not do justice to any of the groups, but is useful in purely general terms. The distinctions between the groups is very hard to describe because the subject is still rife with emotion and pain.  No matter how I describe them, someone will be angered.  Suffice it to say that the British backed the royalist EDES, while all the other groups had to rely upon the people of Greece, and the fortunes of war, for support. The Soviet Union did not support any of the groups, though being so close to the Eastern Front many Soviet small arms found their way into Greece.*
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The main Greek resistance organisation, ELAS - which at their height of power, according to the German army's own records, killed more than 8,000 German soldiers in little over a year, and tied down tens of thousands more. ELAS controlled 80% of the country after Italy capitulated and Germany withdrew. The ELAS then went on to fight the British and other partisan groups, though unsuccessfully due to the fact they were completely outclassed politically. They then became the central opposition to the British/American-backed anti-communist government in the civil war that plagued Greece after WWII.*
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After the EAM/ELAS was disbanded in February, 1945 following a British political victory in propping the EDES up as masters of Greece, the EAM/ELAS formed the Democratic Army of Greece (DAG). At first they fought a guerilla war, but then in 1947-8 sought to meet the National Army on the conventional battlefield. The National Army had been bolstered by billions of US dollars in military aid from the USA and Great Britain in order to present a barrier to the Soviet-controlled lands to the north and north-east.  After some initial successes, the DAG inevitably was splintered and beaten back into Yugoslavia and Albania.*