Greek sprinters Kostas Kenteris and Katerina Thanou have launched a legal challenge against the panel hearing their doping case.
The case is due to reconvene on 22 February
They want Yves Fortier to be removed as president of the Court of Arbitration for Sport (Cas) panel because of an alleged conflict of interest.
Fortier is a business partner of Stephen Drymer, who has worked for the World Anti-Doping Agency (Wada).
And Drymer was a clerk in the Greek sprinters' case before resigning.
The International Council of Arbitration for Sport will now consider the challenge.
If dismissed, the same panel will hear the case when it reconvenes on 22 and 23 February.
But if it is accepted, the composition of the panel will have to change and it is unlikely the case will go ahead on the planned dates.
Gregory Ioannidis, who represents Kenteris and Thanou, said: "Yves Fortier is the president of the law firm that represents Wada in the investigation against Lance Armstrong.
"Mr Drymer was the ad hoc clerk in my clients' case. He decided to resign from his post as a result of the concerns expressed by my clients.
"Mr Kenteris and Ms Thanou are seriously concerned with this unfortunate development. The integrity of the process must be safeguarded at all costs."
But Cas general secretary Matthieu Reeb said he had "full confidence in the independence and impartiality of Yves Fortier".
"He (Fortier) has no relationship personally with Wada," Reeb added.
"And in any case, Wada was not involved in the Kenteris and Thanou case."
The Cas panel in the Kenteris and Thanou case is exactly the same one that recently banned US sprinter Tim Montgomery for two years.
Montgomery has subsequently asked for the ban to be annulled because of an alleged conflict of interest.
Kenteris and Thanou were provisionally suspended by athletics' governing body, the IAAF, in 2004 but the decision was subsequently overturned by an independent Greek tribunal.
The IAAF then appealed to Cas, which will have the final say on the matter.
The Greek sprinters are unhappy at not having been allowed to compete since being provisionally suspended by the IAAF in 2004.
Ioannidis said: "We are failing to comprehend as to why my clients are still suspended, despite the fact that there is a full exoneration at first instance.
"We have analysed the regulatory framework and the conclusion is that the IAAF's current provision on the issue of suspension seriously violates the athletes' rights, as national law and international statutory instruments protect them."