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Thirteen men were killed when British troops opened fire on a group of demonstrators in the Bogside district of Londonderry on 30 January 1972.
The payments, which range from £250 to more than £16,500, were being made "in a spirit of goodwill and conciliation", the Ministry of Defence said.
But the victims' families say they were not seeking compensation, only to clear their relatives of the accusation they were gunmen and bombers.
The riots followed a largely peaceful protest against the policy of internment without trial.
The mood began to deteriorate when some missiles were thrown at troops manning the security barriers and soldiers responded by charging the demonstrators.
The army opened fire, insisting it had been fired on first by two snipers in a nearby tower block.
But the protesters, who were supported by local catholic priest Father Edward Daly, said they were unarmed and most had their backs to the soldiers when the first shots were fired.
An inquiry by Lord Widgery in 1972 completely exonerated the army.
It said their firing had "bordered on the reckless" but there was no doubt they had been shot at first.
Catholic families rejected the inquiry's findings and demanded a fresh investigation.
Speaking after today's decision, Dr Daly, who is now Bishop of Londonderry, said: "I don't think one can put a financial value on a human life. Any life is priceless.
"The government statement says they accept the fact that it's been proved [the demonstrators] weren't carrying weapons but I would have preferred it if they had gone a step further and stated the full truth that these people were completely innocent."
The widow of one of the victims and mother of eight children, Mrs Ita McKinney, is to receive more than £13,000 from the government.
She said: "I will accept the money on behalf of my children. It will not make any difference to my life. I have lost my husband, things will still be the same."
Conservative MP John Biggs-Davison spoke out against the awards. He questioned whether relatives of troops injured in a similar situation would have received as much compensation.
The relatives did accept the compensation money but they continued to fight for a fresh inquiry into the Bloody Sunday killings.
The family of Conservative MP John Biggs-Davison set up a memorial trust after his death in 1988 to help those who had suffered in Northern Ireland.
In December 1992 the Prime Minister John Major wrote to SDLP leader John Hume saying: "The government made clear in 1974 that those who were killed on 'Bloody Sunday' should be regarded as innocent of any allegation that they were shot whilst handling firearms or explosives. I hope that the families of those who died will accept that assurance."
In 1998 Tony Blair's Labour government announced a new investigation, to be chaired by Lord Saville.
It spent two years taking witness statements and ended in November 2004. The final result is expected later in 2005.
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