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The two have been long-time allies and both consider themselves to be leaders of the African continent.
President Mugabe's political opponents claim their spies saw Gaddafi arrive in the country on a Zimbabwe Air Force jet in the early hours of Wednesday morning.
They say the Libyan dictator was taken to a mansion in Harare's Gunninghill suburb, where agents from his all-female bodyguard were apparently seen patrolling the grounds.
This would be very bizarre, indeed.