They argue that the firms supplied equipment used by the South African security forces to suppress dissent.
The companies affected have not yet responded to the judge's ruling.
The plaintiffs argue that the car manufacturers knew their vehicles would be used by South African forces to suppress dissent. They also say that computer companies knew their products were being used to help strip black South Africans of their rights.
The judge disagreed with IBM's argument that it was not the company's place to tell clients how to use its products.
"That level of wilful blindness in the face of crimes in violation of the law of nations cannot defeat an otherwise clear showing of knowledge that the assistance IBM provided would directly and substantially support apartheid," she said.
For the full write up, click on the following BBC link.http://news.bbc.co.uk/2/hi/americas/7991134.stm