David Eastman will learn on Wednesday whether he has successfully removed the judge tasked with deciding whether his second murder trial will go ahead.
Eastman is currently fighting an attempt to put him back on trial for the killing of Assistant Federal Police Commissioner Colin Stanley Winchester in 1989.
He has launched a stay application, arguing that retrial can not possibly take place fairly due to extensive media coverage of the case, the prejudice he suffers from the passage of time, the destruction of exhibits, and the death of witnesses, among other things.
But before that application begins, Eastman is trying to have the judge hearing it removed.
He argues the judge, Acting Justice Anthony Whealy, may be seen to be biased because of his time on the NSW Supreme Court bench with the man who led the original prosecution of Eastman in 1995, Michael Adams.
Acting Justice Whealy ruled against Eastman and kept himself on the case earlier this year, but his decision was appealed to the ACT Court of Appeal.
The Court of Appeal is expected to hand down its judgment on Wednesday morning.
Acting Justices Stephen Walmsley and David Robinson, and Justice Michael Wigney, reserved their decision on the appeal last month.