They said proposals from the new higher education standards watchdog were expensive, unnecessary and at best irrelevant.
The Quality Assurance Agency, however, said its proposals had been backed by students and business leaders.
A consultative document produced by the agency proposes laying down "programme specifications" to show what degrees should cover and setting up a system of registered examiners to inspect university teaching.
The Independent revealed last month that the agency had been forced to back down over inspections after protests from vice-chancellors and lecturers.
Responses from Oxford and Cambridge focus on proposals to set degree standards, which have been criticised as the first step towards a national curriculum for higher education.
Oxford University said it would "strongly oppose" the idea of national specifications for degrees.
The university's response to the consultation said: "We think it highly important to recognise that learning is a two-way process, not simply delivery of a curriculum." Academics said the system "would be highly expensive and without benefit in this or similar institutions".
Cambridge said: "It would be nothing short of disastrous if the system proposed ... were to have the effect of crippling those institutions whose expectation is excellence and whose performance is outstanding. There is a serious risk that the present proposals would do just this."
John Randall, chief executive of the Quality Assurance Agency, said that proposals would be developed in the light of the 300 responses to the consultation.
"There are proper concerns that a new system should be effective, not bureaucracy," he said. "It should build on what has been achieved by institutions and avoid duplication of effort. It must recognise the diversity that gives higher education its strength."
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