Yes! The normal child care tax credit requirements apply. You might qualify for a credit for the child care expenses paid to a foreign care provider so that you (and your spouse) can work or look for work.
However, you must have earned income on your U.S. tax return to claim the child care tax credit. If you were able to reduce all of your taxable income using the foreign earned income exclusion, then you cannot claim the child care credit. But if you have earned income on your tax return after applying the foreign earned income exclusion, you can claim the child care tax credit on your U.S. expat tax return.
Additionally, you're not obligated to provide a tax identification number for a foreign childcare provider like you are when living in the U.S.
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