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Mr Smith made the Unilateral Declaration of Independence (UDI) after days of tense negotiations with British Prime Minister Harold Wilson.
His address to the people of Rhodesia said he had taken the action, "so that dignity and freedom of all may be assured".
After the proclamation he explained: "There can be no happiness in a country while the absurd situation continues to exist where people, such as ourselves, who have ruled themselves with an impeccable record for over 40 years, are denied what is freely granted to other countries."
British authorities were only prepared to permit independence on the basis of giving the black majority population a fair share of power.
Under Mr Smith's system there will be white minority rule, where 220,000 white Rhodesians will enjoy privileges over nearly four million black Rhodesians.
Harold Wilson told a packed and solemn House of Commons the Labour Government would not be sending troops to deal with the crisis.
Instead he announced a full-range of sanctions including ceasing all British aid to and preferential treatment for Rhodesia, banning the import of Rhodesian tobacco and recalling the British High Commissioner.
Both Rhodesian opposition parties - the Zimbabwe African National Union (Zanu) and the Zimbabwe African People's Union (Zapu) have declared breakaway governments.
They have both called upon the British Government to use force to suspend the Smith Government.
Zanu has also petitioned the United Nations and the Organisation of African Unity for assistance.
Zapu National Treasurer Jason Mayo gave a statement before leaving London - where he has been in exile - to set up his rival government in Lusaka, Zambia.
"Treason and rebellion have been committed. The lives particularly of four million unarmed Africans are in jeopardy," he said.
The Kenyan Government has offered support to "our African brothers in Southern Rhodesia", but did not refer specifically to Zanu or Zapu.
The next day the United Nations Security Council condemned Mr Smith's regime in Rhodesia.
The US immediately supported the British sanctions - with embargoes on arms exports and sugar imports - and the UN called for all its members to implement economic sanctions in 1966.
France and the USSR abstained, but South Africa and Portugal - with its colony Mozambique - refused and their continued trading with Rhodesia was instrumental in keeping the Smith government afloat.
Joshua Nkomo's Zapu and Robert Mugabe's Zanu parties overcame their differences to form the Patriotic Front (PF) to confront Ian Smith.
Armed resistance from their guerrilla movements continued until white rule formally ended in June 1979, when Abel Muzorewa of the African National Congress (ANC) became the first black prime minister of the newly named Zimbabwe-Rhodesia.
Robert Mugabe was elected prime minister of an independent Zimbabwe in 1980 under a new constitution.
Mr Smith remained an MP until 1987.
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