Two Korean-Americans in the U.S. Army, one a U.S. citizen, the other a legal permanent resident, are being pursued by South Korea as draft dodgers for failing to complete mandatory military service in Korea. The nations are currently at a bit of a legal impasse on their status. This is likely further complicated by the fact that military service in the U.S. puts you on a fast track to U.S. citizenship, thus, even the Korean-American soldier who is not now a U.S. citizen, will likely be one by the time his tour of duty is over. Citizenship, however, is apparently not a great concern to the South Korean draft board which has its own standards in such matters.
Korean military service is apparently more onerous than American military service, although hearing stories about their days serving from my father, who was an American military conscript, and my father-in-law, who served in the South Korean military conscript, it isn't obvious that this has always been the case.