Rambus specializes in technology that speeds the transmission of data between computer chips.
'Olive branch'
Shares in Hynix fell 1.92% to 33,250 won following the decision while Samsung, the
world's biggest maker of memory chips, fell 1.93%.
After the legal ruling Hynix said it would appeal against the federal court decision.
It said its appeal would focus on "whether or not Rambus violated anti-trust laws in acquiring and enforcing these patents".
"In the next phase, scheduled for this summer, Hynix will seek to have all of the Rambus patents in dispute held (to be) unenforceable," Hynix said.
The damages cover Hynix memory chip sales between the summer of 2000 and the end of 2005, Rambus said.
"We continue to hold out an olive branch to resolve these matters short of full scale trials," said Rambus general counsel John Danforth.
"By doing this, we give defendants and potential defendants a way to avoid significant exposure to antitrust and patent cases," he added.
The Hynix case went to trial a month ago after six years of legal wrangling.