Since the United States no longer launches war with a declaration, it is a somewhat slippery business to determine the starting and ending dates, but the war in Afghanistan appears to be challenging Vietnam for the title of longest war as measured by combat involving American troops.
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The demilitarized zone near the 17th parallel was established after the defeat of France in Indochina as a buffer separating North and South Vietnam. Afghanistan was invaded in 2001 as a result of the refusal of its Taliban government to reject Osama Bin Laden. The United States slid slowly into the position previously held by France in Indochina and became engulfed in a long war in Vietnam. After the French proved themselves unable to recover their Indonesian territory after World War II, the United States gradually took on their role and became mired in a land war.