Cyrenaica Defense Forces Company -- elite forces trained, assisted and advised by British military specialists.  Responsible for the defense of the Cyrenaica region.*
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The police paramilitary forces during the Libyan monarchy were composed mainly of conservative tribal elements.  They were designed by King Idris to be more reliable than the regular army.  Their primary mission was to counter balance the dissident factions within regular army, and prevent any coup against the monarchy.*
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Prior to the September 1969 coup by Qadhafi, all armour and artillery was in the possession of the police paramilitary.  After Qadhafi's coup, the police paramilitary was absorbed into the regular army almost immediately.