Sixth-formers wanting to study English or Philosophy, Politics and Economics (PPE) at Oxford will sit extra exams for the first time from the end of this month.
The Association of School and College Lecturers said that the growth in the number of Oxbridge entrance exams puts state school pupils at a particular disadvantage.
The accusation came as Oxford and Cambridge suffered renewed attacks for failing to recruit more state school students.
The Institute for Public Policy Research said that on current trends, neither would hit their 2011 targets for widening access.
The think-tank said state pupils getting three As at A-level were "significantly under-represented" at both universities and called on them to be more proactive and to "stop blaming a lack of applications for their failure to make progress".
But the universities said the research was flawed because it assumed all A grades were equal and did not take into account the suitability of different subject combinations. They also argued that because around a fifth of pupils now achieved three A grades, A-levels alone are no longer an adequate basis for deciding admissions.
Oxford has already introduced aptitude tests in law, medicine, maths, physics, history and computer science.
At Cambridge, the number of applicants taking the "thinking skills" test in subjects including economics, engineering and natural sciences has risen to more than 3,000.
John Dunford, ASCL general secretary, said the tests were reasonable for courses such as law and medicine, which sixth forms might not offer. But in other subjects, access to marks in individual A-level modules ought to be sufficient.
"The increase in tests is a real problem, particularly for maintained schools," he said. "There would be an expectation that you put on extra classes, but that is difficult for schools that only send one or two pupils to Oxbridge a year."
The tests help explain why just 100 elite schools account for a third of all Oxbridge admissions, as the Sutton Trust revealed last month.
The introduction of A-star grades is also expected to make private school pupils fare better in admissions. An AQA exam board study, published last month, found that fee-paying pupils would get a third of the A-star grades awarded.