This is a broad question. Let us address it in a logical way:
  1. Nonimmigrants:
    1. Extension of Status situations: An individual can travel when the INS is processing a petition for extension of status, provided the individual has an unexpired visa to travel and return to the United States.
    2. Change of Status situations: Travel is prohibited if the individual has applied for a change of status. The change of status application is considered abandoned if the individual leaves the United States when the Petition is pending with the INS.
    3. Travel Under Portability: In a memo dated, January 29, 2001, Michael A. Pearson, Associate Commissioner, Office of Field Operations, outlined the requirements for admission of an individual at a Port of Entry. The memo states that an H-1B applicant for admission, who is no longer working for the original petitioner is admissible pursuant to portability provisions of AC21, as long as he meets certain requirements:
      • Is otherwise admissible
      • Is in possession of a valid visa and unexpired passport
      • Satisfies the POE officer that he was originally admitted as an H-1B nonimmigrant.
      • Presents evidence in the form of a receipt that a new H-1B petition has been filed and is pending with the Service center.
  2. Immigrants:
    On June 1, 1999, the legacy Immigration and Naturalization Service published an interim rule at 64 Federal Register 29209. The rule amends the previous Service policy statements regarding the eligibility of H-1 and L-1 [there is a move to extend this to F, E and O visa holders] nonimmigrants, and their dependent family members, to maintain and to extend their nonimmigrant status while their applications for permanent residence remain pending.

    This rule also addresses the issue of the eligibility of these aliens to travel outside the United States without their applications for Adjustment of Status. As long as H-1 and L-1 nonimmigrants remain compliant with their nonimmigrant classification, including restrictions on periods of stay, change of employer and engaging in employment, the mere fact that they have filed an application for adjustment of status does not make them ineligible for extensions or applicable changes to their nonimmigrant status Further, the rule also amends Section 245 by providing that an H-1 or L-1 nonimmigrant with a pending application for adjustment of status no longer needs to seek advance parole to travel abroad. An H-1 or L-1 nonimmigrant may be readmitted to the United States in the same status provided that her or she has a valid H-1 or L-1 visa, has the original I-797 receipt notice for the I-485 filing, and remains eligible for H-1 or L-1 classification.