Each country has its own policies regarding dual citizenship and renunciation of nationality. Although the oath of allegiance that new U. S. citizens take states that they are renouncing all other governments, often that has as much weight in their home country as a similar oath taken by an American would have in the eyes of the U. S. government. Just as those wishing to renounce U. S. citizenship must follow specific steps, so must those who are giving up another nationality.
In the case of those who have citizenship ties to another country through means other than birth or naturalization, it is a good idea to check with that country. If a country recognizes as a citizen anyone who had one parent who was a citizen, it is possible that a lifelong American could inadvertently possess dual citizenship. This fact does not suggest that countries are lying in wait for innocent tourists who, on a visit to their ancestral home, find out that they must serve three years in the military before they can leave. But depending on the stability of the government in question, it may be a good idea to speak to someone in the consular offices in the United States to make sure there will be no unforeseen problems. If, for example, a particular country recognizes a dual national solely as one of its citizens and that person is charged with a crime while in that country, U.S. citizenship will be of little if any value.