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In military terminology, a two-front war is one in which fighting takes place on two geographically separate fronts. It is usually executed by two or more separate forces simultaneously or nearly simultaneously, in the hope that their opponent will be forced to split their fighting force to deal with both threats, therefore reducing their odds of success. Where one of the contending forces is surrounded, the fronts are called interior lines.
Ancient times 
One of the earliest examples of a two-front war occurred in the third century BC, when the Roman Republic fought the First Macedonian War contemporaneously with the Second Punic War against Carthage. Also, after the consolidation of the Empire's frontier in the reign of Augustus, the Roman forces had to contend with multiple enemies in its frontiers, in the Rhine, the Danube and Mesopotamia, with various examples of emperors (such as Septimius Severus and Aurelian) who marched their armies from one side of the Empire to another to face them. In the later period, after the collapse of the Western Roman Empire, the surviving part, the Byzantine Empire had to face invaders coming from both west and east and simultaneously trying to preserve its territories in Italy.
Napoleonic Wars 
During the Napoleonic Wars, France repeatedly fought on multiple fronts. For example, France fought the Spanish and British in the Peninsular War while fighting the Russian Empire at the same time during its invasion of Russia.
World War I 
During World War I, Germany under Kaiser Wilhelm II fought a two-front war against French, British, Belgian, and (later) American forces on the Western Front while simultaneously fighting the Russians on the Eastern Front, until the Bolshevik Revolution of 1917 took Russia out of the war. Germany had foreseen such a scenario, and developed the Schlieffen Plan in order to counteract being surrounded by its enemies. Under the Schlieffen Plan, German forces would invade France via Belgium, Luxembourg, and the Netherlands (the idea to go through the Netherlands was abandoned because of the country's neutrality), quickly capturing Paris and forcing France to sue for peace. The Germans would then turn their attention to Russia in the east before the Tsar could mobilize his massive forces. Due to several factors however, the Germans failed to achieve the plan's aims.
World War II 
Perhaps the most famous example of a two-front war was the European theatre during World War II, when Hitler's Nazi Germany had to deal with the Western Allies on the west and the Soviet Union to the east. The Germans were unable to repel either of the two front's advances and eventually lost the war. While there were other contributing factors, such as the insufficiency of the Wehrmacht for a long war, and the abandonment of blitzkrieg tactics due to fuel shortages and a rising need to defend territory, the two-front war was an important factor in deciding when the German military would be forced to surrender.
The Allies, especially the United States, also fought a two-front war, splitting their forces between the European theatre against Nazi Germany and the Pacific War against Japan. Japan too was fighting in both Asia and the Pacific. The Axis Powers had the opportunity to force the Soviet Union into a two-front war by means of a Japanese attack on the Soviet Far East, but the Japanese declined to do so, due to their defeats in the Soviet–Japanese border conflicts. While Germany and the United States remained respective threats, the Soviets and Japanese did not fight each another until the August 9 Soviet-Japanese War (1945), three months after the surrender of Germany. In the case of the United States, the Pacific theatre was primarily a naval and air effort despite losing ships during the 1941 Pearl Harbor Attack while ground forces were used in Europe.
Israeli-Arab Wars 
In the 1948 Israeli-Arab War, the Israelis fought the Egyptians to the south and the Jordanians and Syria in the east and north. Israel again fought two-front wars in the Six-Day War of 1967 and the Yom Kippur War of 1973.
Cold War 
A major rationale for the American 600-ship Navy plan in the 1980s was to threaten the Soviet Union with a two-front war (in Europe and the Pacific Ocean) in the event of hostilities.