In order to claim your children as dependents, they must be a US citizen or resident or a resident of Canada or Mexico.
In order for them to be considered a resident, they will have to meet the substantial presence test or be a green card holder. This is the same test for everyone to be a resident of the US unless they are exempt under certain visas. Please see the following:
Use the following calculation for the substantial presence test, count all the days of 2017 that they were in the US, count 1/3 of the days they were in the US in 2016 and count 1/6 of the days they were in the US in 2015. If the days add up to 183 US days or more, then they are a US resident for tax purposes.
