If yours has expired, you will have to apply for a new one at a United States consulate abroad. Your dependents will need J-2 visas, and you should be prepared to show proof of marriage to your spouse and parenthood of each child. Extending your stay without leaving the country. First, fill out and sign the back of the white page of your new Form IAP-66. Then proceed either by notification or by application .
Notification is more convenient.
That will complete your extension. Application is much less convenient. Disregard the first paragraph of that section, which tells you to mail J extensions to your local INS office. That practice has been changed since Form I-539 was last revised. Send the application via some kind of secure mail that will give you a receipt.