Category 1
Emergency Leave Unfunded Travel. Transportation by the most expeditious routing only for bona fide immediate family emergencies, as determined by DOD Directive 1327.5. This travel privilege shall not be used in lieu of a funded travel entitlement.

• Uniformed Services members with emergency status indicated in leave orders.
• U.S. citizen civilians stationed overseas and employees of the Uniformed Services/ Nonappropriated Fund (NAF) activities and whose travel from the CONUS, Alaska or Hawaii was incident to a PCS assignment at NAF expense.
• Dependents of members of the Uniformed Services when accompanied by their sponsor.
• Dependents, command sponsored of :
• U.S. citizen civilian employees of the Uniformed Service, stationed overseas
• U.S. citizen civilian employees of the DoD stationed overseas and paid from NAF, or
• American Red Cross full-time paid personnel serving with a DOD Component overseas.

Category 2
Sponsors in an Environmental Morale Leave (EML) status and their dependents traveling with them, also in EML status.  Sponsors includes:

• Uniformed Services Members.
• U.S. citizen civilian employees of the Armed Forces who are eligible for Government-funded transportation to the United States at tour completion (including NAF employees).
• American Red Cross full-time, paid personnel on duty with DOD Component overseas. 
• USO professional staff personnel on duty with the Uniformed Services.
• DODDS Teachers during the school year and for Employer-approved training during recess periods.

Category 3
Ordinary Leave, Close Blood or Affirmative Relatives, House Hunting Permissive TDY, Medal of Honor Holders, Foreign Military, and Others.      

• Uniformed Services members in a leave or pass status, other than emergency leave, including members of the reserve components on active duty, in leave or pass status.
• Dependents of a member of the Uniformed Services when accompanied by their sponsor in a leave status.
• Uniformed Services members traveling under permissive TDY orders for house hunting incident to a pending PCS. 
• One dependent may accompany a Uniformed Services member.
• Medal of Honor recipients and their dependents (when accompanied by their sponsor).  Except for active duty, traveler shall present a copy of the Medal of Honor Award Certificate.
• Foreign cadets and midshipmen attending U.S. Service academies, in a leave status.
• Foreign Exchange Service members on permanent duty with the DoD, when in a leave status.
• Dependents of foreign exchange Service members on permanent duty with the Department of Defense when accompanied by their sponsor. 

Category 4
Unaccompanied Dependents on EML and DODDS Teachers on EML During Summer.

• Dependents traveling under the EML Program, unaccompanied by their sponsor.
• DODDS teachers of dependents accompanied or unaccompanied traveling under the EML Program. 

Category 5
Permissive TDY (Non-House Hunting) Students, Dependents and Others.

• Military personnel traveling on permissive TDY orders other than for house hunting.
• Dependents (children) who are college students attending in residence at an overseas branch of an American (U.S.) university located in the same overseas area in which they reside, command sponsored, stationed overseas with their sponsor, who is: (1) A member of the Uniformed Services; (2) A U.S. citizen civilian employee of the Department of Defense (paid from either appropriated funds or NAF); or (3) An American Red Cross full-time, paid employee serving with the Department of Defense.
• Dependents, command-sponsored, stationed overseas with their sponsor who is: (1) A member of the Uniformed Services; (2) A U.S. citizen civilian employee of the Department of Defense (paid from either appropriated funds or NAF); or (3) An American Red Cross full-time, paid employee serving with the Department of Defense. Unaccompanied travel is permitted to and from the nearest overseas military academy testing site to take scheduled entrance examinations for entry into any of the U.S. Service Academies...

Category 6
Retired, Dependents, Reserve, ROTC, NUPOS and CEC

• Retired Uniformed Services members
• Dependents of retired Uniformed Service members, when accompanied by their sponsor.
• Dependents, command sponsored, stationed overseas with their sponsor who is: (1) A member of the Uniformed Services; (2) A U.S. citizen civilian employee of the Department of Defense (paid from either appropriated funds or NAF); or (3) An American Red Cross full-time, paid employee serving with the Department of Defense. Unaccompanied travel is permitted to the U.S. for enlisting in one of the Armed Forces when local enlistment in the overseas area is not authorized. If an applicant for Military Service is rejected, return travel to the overseas area may be provided under this eligibility.
• Authorized Reserve component members and authorized Reserve component members entitled to retired pay at age 60 (gray area retirees) traveling in the CONUS and directly between the CONUS and Alaska, Hawaii, Puerto Rico, the U.S. Virgin Islands, Guam, and American Samoa (Guam and American Samoa travelers may transit Hawaii or Alaska); or traveling
within Alaska, Hawaii, Puerto Rico or the U.S. Virgin Islands
• Newly commissioned ROTC officers who are awaiting call to extended active duty.  Travel is authorized within and between the CONUS, Alaska, Hawaii, and the U.S. territories

Source: DoD 4515.13-R, Air Transportation Eligibility