AFP confirmed the lawsuit, initially reported by the Financial Times, with a source close to the issue.
The family is accusing the investors, Hong Kong-based Integrated Whale Media Investments, of refusing to pay a large amount of the promised price.
US media said the deal, announced in mid-2014, valued Forbes Media at $475 million.
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At the time of the announcement the publisher of Forbes magazine said that the Forbes family will retain "a significant ownership stake" in the company under the plan and will continue to participate in its operations.
The majority stake of the Asian investors was not made public.
The magazine, known for its rankings of wealthy Americans and global business leaders, was launched in 1917 by Scottish immigrant BC Forbes. It was run by his son Malcolm Forbes before being taken over by Steve Forbes, a onetime presidential candidate.
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The magazine has some six million readers in the United States and international editions published in 21 languages, which brings the number of global readers to some 75 million.
The agreement had Forbes lending money to the investors to finance the deal, according to the lawsuit filed in a Maryland court that AFP consulted.
The investors, however, have not made full regular payments, the lawsuit contends, and now the family wants payment in full.
Integrated Whale rejected the charges in an email to AFP as baseless and without merit.
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