The High Court will consider the latest legal action brought by killer Jeremy Bamber in his fight to overturn his convictions for murdering five relatives more than 25 years ago.
Two judges in London will hear a judicial review application.
Bamber wants to challenge a refusal by the Criminal Cases Review Commission (CCRC), the independent body which investigates possible miscarriages of justice, to refer his case back to the Court of Appeal to be looked at again.
The hearing follows the rejection by a single judge, who studied the case papers in private, of Bamber's application for permission to seek judicial review of the CCRC's decision.
His renewed application will be dealt with by Sir John Thomas, president of the Queen's Bench Division, and Mr Justice Globe.
Bamber, 51, who is serving a whole-life term for the 1985 killings, has always protested his innocence and claims his schizophrenic sister Sheila Caffell shot her family before turning the gun on herself in a remote Essex farmhouse.
Announcing its decision in April, the CCRC said that despite a lengthy and complex investigation, it "has not identified any evidence or legal argument that it considers capable of raising a real possibility that the Court of Appeal would quash the convictions".
:: Bamber and two other murderers are involved in a European court battle against their "whole-life" prison terms - which give prisoners no chance of release.
Lawyers are urging judges in Strasbourg to rule that UK law allowing the most dangerous offenders to be kept behind bars until they die breaches their human rights.