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@mgpu wrote:

Question1:

I have a J-1 Visa and work as a teacher . . . my husband has a J-2 Visa with a work permit and worked as an independent contractor.  Does my husband have to file as a Non-Resident alien or Resident Alien for tax purpose when he was here for a total of 365 days in the U.S. 

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The US tax residency status of the spouse on J-2 who has work authorization is determined the same way as the taxpayer who is on J-1 so long as they substantially comply with the conditions of their visas.

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@mgpu wrote:

We have two children and can they apply for an Itin number if the taxes are filed as a Non-Resident or Resident? 

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If there is a tax purpose for the children to have an ITIN, they can then apply for one.  Otherwise, no.