This article is from the FAQ, by with numerous contributions by others.
Note: The following comment focuses on Indian nationals. But, it can
be equally applicable to people from any country.
1. Begin the process well in advance of the expiration of your visa. Six
months to a year ahead would be a good idea.
2. Contact your regional (Indian) consulate for the application forms for
obtaining the "no obligation to return (to India)" (NORI) statements.
3. Fill out the forms in quadruplicate (instructions provided), have them
notarized and send them back to the consulate.
4. The consulate will return the forms with its endorsement and a letter
stating that you need to get clearance from 3 agencies (in India)
(addresses provided). These agencies are:
1. Your local passport office
2. Home minister of your state government
3. Dept. of Education, Ministry of Human Resources, New Delhi
Note: If you are a practicing medicine you need to get an additional
clearance (Ministry of Health, I believe)
5. Send the forms to India and preferably have your family personally get
these clearances. You may need to get clearances from the
police and tax authorities.
6. Each of those agencies will send back a NORI statement to you and
simultaneously to the (Indian) consulates in US.
7. Send the NORI statements to your regional consulate. They will forward
a letter to the (Indian) Embassy.
8. The (Indian) Embassy will send a NORI statement to the United States
Information Agency (USIA).
9. The USIA will send you a form to fill. Return this form to them.
10. The USIA will make a recommendation and send it to the Immigration and
Naturalization Service (INS).
11. INS will issue the final waiver.
The process after getting the NORI statements (from India) takes about 3
months. The process of getting the NORI statements (from India) could
take anywhere from three weeks to a few months,
(Maybe it would be better to get these clearances done yourself
if you go on vacation).
 
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