jamahiriyawikimedia commons
Muammar el-Qaddafi continues to claim that he can't resign because he's not a president and that Libya is and always has been controlled by the people.

So what exactly is a Jamahiriya?

From Wikipedia:

Jamahiriya (Arabic: جماهيرية‎ jamāhīriyyah) is an Arabic term generally translated as "state of the masses". The term, a neologism coined by Muammar al-Gaddafi in The Green Book, is intended to be a generic term comparable to a People's Republic, and describing the form of statehood of Libya.

In the official political philosophy of Libya, this system is unique to the country, although it is the materialization of the Third International Theory, proposed by Gaddafi to be applied to the entire Third World. The term in practice has only been applied to the Libyan state, of which Gaddafi is the Caid (translated Leader; strict transliteration Qāʾid). Although Gaddafi no longer holds public office or title, he is accorded the honorifics "Guide of the First of September Great Revolution of the Socialist People's Libyan Arab Jamahiriya" or "Brotherly Leader and Guide of the Revolution" in government statements and the official press.[1]

In other words Qaddafi made it up, he makes the rules.