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The following 5 scenarios are not subject to the annual quota. You can apply now for an H-1B Visa if:
Employer is an institution of higher education (College or University).
Employer is a nonprofit organization or entity related to or affiliated with an institution of higher education (Hospital affiliated with a University).
Employer is a nonprofit research organization or a governmental research organization.
You are a J-1 nonimmigrant alien who received a waiver of the 2-year foreign residency requirement.
You have been previously granted status as an H-1B nonimmigrant in the past 6 years and not left the U.S. for more than a year after attaining such status (H-1B Renewals and Transfers).