Fedusa and Saptu have asked Higher Education Minister Blade Nzimande to include them in the committee on transformation of the higher education sector.
"We believe that the minister would make a strategic error if he continues with the current structure of the committee," Federation of Unions of SA general secretary Dennis George said in a statement on Thursday.
"Although we are glad that trade unions are involved, we believe that the current composition is not representative of university staff holding positions at our universities."
SA Parastatal and Tertiary Union (Saptu) general secretary Ben van der Walt said his union should also be represented in the committee, as it was a majority union and an important stakeholder at various institutions.
"We are an inclusive union and we have proven ourselves to have truly transformed.
"We represent academics and support staff at universities, and our members represent the demographics of our country. We pride ourselves in our diversity," he said.
On Wednesday, Nzimande said he had set up a transformation committee for universities, nearly five years after a probe sparked by a racist incident in the Free State.
Part of the committee's job would be to review initiation practices at universities.
The probe into discrimination in universities was conducted after a racist incident at the University of the Free State (UFS) in February 2008.
A video emerged of UFS employees undergoing an initiation, which included having to get on their knees and eat food which had apparently been urinated into by male students at the Reitz men's residence.
George said the only way to deal with this issue was by being inclusive.
"By not including all parties, the committee might become simply irrelevant. The results of the investigation, as well as the eventual impact of recommendations will then certainly be compromised," he said.
Fedusa and Saptu sent a letter to Nzimande with their request. They offered to, if necessary, meet Nzimande.