This section is from the book "The Constitutional Law Of The United States", by Westel Woodbury Willoughby. Also available from Amazon: Constitutional Law.
In time of war, and especially upon the actual theatre of war, military courts have, without express legislative authorization, exclusive jurisdiction over the members of the military forces. As the court say in Coleman v. Tennessee :16 "In denying to the military tribunals exclusive jurisdiction under the section of the law of Congress in question, over the offenses mentioned, when committed by persons in the military service of the United States and subject to the Articles of War, we have reference to them when they were held in States occupying, as members of the Union, their normal and constitutional relations to the Federal Government, in which the supremacy of that government was recognized, and the civil courts were open and in the undisputed exercise of their jurisdiction. When the armies of the United States were in the territory of insurgent States, banded together in hostility to the national government and making war against it, in other words, when the armies of the United States were in the enemy's country, the military tribunals mentioned had, under the laws of war and the authority conferred by the section named, exclusive jurisdiction to try and punish offenses of every grade committed by persons in the military service. Officers and soldiers of the armies of the Union were not subject during the war to the laws of the enemy or amenable to his tribunals for offenses committed by them. They were answerable only to their own government, and only by its laws as enforced by its armies could they be punished."
16 97 U. S. 509; 24 L. ed. 1118.
 
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