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The Government Accountability Office said the Pentagon was one of several departments where "legacy systems" urgently needed to be replaced.
The report said taxpayers spent $61bn (£41bn) a year on maintaining ageing technologies.
It said that was three times more than the investment on modern IT systems.
The report said that the Department of Defence systems that co-ordinated intercontinental ballistic missiles, nuclear bombers and tanker support aircraft "runs on an IBM Series-1 Computer - a 1970s computing system - and uses eight-inch floppy disks".
"This system remains in use because, in short, it still works," Pentagon spokeswoman Lt Col Valerie Henderson told the AFP news agency.
"However, to address obsolescence concerns, the floppy drives are scheduled to be replaced with secure digital devices by the end of 2017."
She added: "Modernisation across the entire Nuclear Command, Control, and Communications enterprise remains ongoing."
The report said that the Pentagon was planning to fully replace the system by the end of 2020.
According to the report, the US treasury also needed to upgrade its systems, which it said was using "assembly language code - a computer language initially used in the 1950s and typically tied to the hardware for which it was developed".