As a resident alien for tax purposes you will follow the same rules and file the same forms as US citizens. Here is a link for reference. You can claim your dependents, but they must have social security numbers or Individual Taxpayer Identification numbers.
NOTE: An ITIN does not qualify a child for Earned Income Credit or the Child Tax Credit; but will help qualify them for the "Other Dependent" credit.
They must have lived with you in the US for more than 1/2 the year.
Here is a link with information on applying for an ITIN if needed.
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