You didn't say where you live, or whether your nephews live with you. You might be able to claim your nephews as dependents, but just being your dependents does not make them qualifying children for the Earned Income Credit (EIC or EITC). To be qualifying children for EIC they have to have lived with you in the United States for more than half the year. That is obviously not the case, since they have never been to the United States. so you cannot use them for EIC.
You can use the tool at the following link on the IRS web site to determine whether you can claim your nephews as dependents.
Whom May I Claim as a Dependent?
