The new royal baby is the first to qualify for both a British and US passport - bit might also face paying US taxes.
Mum Meghan's American birth means her son can also claim citizenship - but that might mean he has to one day pay taxes.
The US is unusual in that it still taxes its citizens even if they live in foreign countries.
This could pose challenges for the royals further down the line, with gifts between them possibly becoming taxable.
But, potential headaches aside, the new royal also retains the right to become a US citizen.
In order for this to become a reality, Harry and Meghan would need to register the birth at an American consulate.
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Conversely, Meghan can apply to become a UK citizen after five years in the country.
If she then decides to renounce her US citizenship she would have to pay what is known as an "exit tax", reports The Sun .
Speaking previously about the tax situation, tax lawyer Stuart E. Horwich told CBS MoneyWatch: "When a child is born a U.S. citizen, they are a U.S. taxpayer irrespective of residency,"
"The kid will have to list all foreign bank and financial accounts in which he or she has an interest."
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But despite the lack of historical precedent, experts said they expect the royal household to be prepared for dealing with US tax authorities.
California attorney Robert Wood said: "They are certainly going to be getting top-quality tax advice, and I would hope and am sure they are doing it all right, even though it's an unusual event for the British Royal family to be filing things with the IRS."
