...You sure the key words aren’t “that may be born beyond the sea, or out of the limits of the United States” aren’t the key words?...
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Speaking of key words.... are the children, born overseas to two American citizen parents, legally subjects of America at the time of their birth?
mlo can reply also should he/she so desire.
Now or then?
Legally speaking, not unless the parents take some kind of necessary action, such as obtaining a Certification of Live Birth and duly registering the event on a form supplied by the local U.S. embassy or consulate.