The answer is whatever jurisdictiion SA has will control.
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In general terms, any country that would allow a citizen to hold dual US citizenship would recognize a divorce legally obtained in the US. However, as my colleagues have answered, to be absolutely certain you would need to confer with an attorney in South Africa, as well as to determine what steps, if any, are necessary for recognition to occur (some countries have very specific processes and requirements).
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Most jurisdictions around the world recognize divorces that observe the same vague formalities as in that jurisdiction. The US recognizes marriages as long as similar vows were made to that of a US marriage. You would need to look at the law of South Africa. My guess is that they will recognize a US marriage, but I don't know for sure.