Dependents are allowed to stay on the parents policy up to the age of 26. After that, they must find their own policy which will shortly be attainable through the insurance marketplace. I would encourage you to work with a local agent regarding the marketplace as well as other options available.
Your children can remain on your health insurance plan until age 26. After that they would need to apply for their own plan. Good news is! They are eligible to obtain coverage through the marketplace and qualify for the SEP (Special Enrollment Period).
Depending on their income, they may also qualify for tax credit's as well!
Depending on their income, they may also qualify for tax credit's as well!