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But the deal will only go ahead if Mr Murdoch can reach a deal with the print unions over the introduction of new technology within the next three weeks.
He has also threatened to pull out of the sale if it is referred to the Monopolies and Mergers Commission.
But this seems less likely now that Mr Murdoch has received the backing of Thomson British Holdings, the company seeking to sell Times Newspapers on behalf of Lord Thomson of Fleet.
New printing plant
Mr Murdoch said he thought it would take several years to bring the paper back into profit - but he regarded this new challenge as "the most exciting one of my life".
The Australian tycoon, who already owns The Sun and News of the World, as well as a string of newspapers and broadcasting stations in the United States and Australia, is building a big new printing plant in East London.
There has been speculation that as well as the two British tabloids, he could print The Times newspapers there as well.
Joe Wade, general secretary of the National Graphical Association, said he was confident an agreement could be reached within the three-week deadline.
The newspapers are in danger of closing if a deal cannot be reached so the unions seem unlikely to oppose Mr Murdoch's plans.
Mr Murdoch will be expected to meet a number of conditions aimed at preserving the editorial integrity of the papers.
These include no restraints on freedom of expression and freedom from attachment to any political party.
For the past four years Mr Murdoch has lived in New York where his American flagship newspaper, the New York Post, has been a considerable drain on his resources.
But Mr Murdoch has drawn criticism for the paper's dramatic switch from being the voice of the liberal leaning Democrats to campaigning for Ronald Reagan and right-wing Republicanism.
The paper has also paid more attention to sex scandal and crime stories than it did in the past.
This has led to speculation about what a Murdoch proprietorship might mean for The Times.
Rupert Murdoch was formally confirmed as the new owner of The Times and Sunday Times on 12 February 1981 after reaching agreement with the unions. The deal led to 563 redundancies.
MPs had earlier agreed to let the deal go ahead without referring it to the Monopolies and Mergers Commission (MMC).
The then Trade Secretary John Biffen defended his decision not to refer the deal to the MMC on the grounds that the alternative could have meant the closure of the Times titles with 4,000 redundancies.
Mr Murdoch pressed ahead with the introduction of new technology - which meant moving the production of the papers to his new plant at Wapping in east London.
The move led to months of angry protests at the plant as 4,000 print workers faced redundancy, but Mr Murdoch won the battle and not a single day's production was lost.
By 1988 all Britain's national papers had moved out of Fleet Street and adopted new, cheaper printing technology.
William Rees Mogg had already signalled his intention to step down as editor of The Times and was replaced by Harold Evans, who was editor of The Sunday Times.
However Mr Evans remained in the post only a year before resigning over differences about editorial policy.
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