According to Bill Cooper, Maji is the MAJORITY AGENCY FOR JOINT INTELLIGENCE. All information, disinformation, and intelligence is gathered and evaluated by this agency. This agency is responsible for all disinformation and operates in conjunction with the CIA, NSA, and the Defense Intelligence Agency. This is a very powerful organization and all alien projects are under its control. MAJI is responsible only to MJ-12. (MW Cooper)

Quite often the word "Majestic" is used instead of MAJI. It's a covert organisation. It was decided that knowledge about alien civilisations on Earth could have devastating effects on major parts of society (cf. Brookings Report). Therefore an organisation was created to consequently keep this information from the public. This organisation was Maji / Majestic. However, over the years it has been infiltrated by secret government people and people associated with the "negative" aliens. Nowadays, it has a mixed agenda.

It can safely be assumed that not only within the USA such a group was created. Several authors claim that the heads of the international alien cover-up groups form the Bilderberger Group, named after the hotel in Holland where they first met (in the early 50's).