Murderer Jeremy Bamber and two other killers have begun their appeal in the European Court of Human Rights against spending the rest of their lives in prison.
Bamber was jailed for murdering five members of his family in Essex in 1985.
Serial killer Peter Moore and Douglas Vinter, who killed his wife 13 years after murdering a colleague, are also challenging the court rulings.
They say the whole life tariff is "inhuman and degrading".
The verdict will not be announced until next year. Decisions from the court often take up to nine months to consider.
The three men are among a group of 43 prisoners who have been given whole life tariffs, meaning they cannot be released other than at the discretion of the secretary of state on compassionate grounds - for example, if they are terminally ill or seriously incapacitated.
They claim that denying them any prospect of release amounts to "inhuman and degrading" treatment and they should be entitled to have their tariffs reviewed.
The case was referred to the Grand Chamber after the men narrowly lost their first European Court hearing earlier this year: three of the seven judges ruled in their favour.
Last week the Court of Appeal in London upheld the principle of the whole life tariff, saying it was a "draconian penalty" reserved for cases of "exceptionally serious criminality".
This case has the potential to put the Strasbourg court on another collision course with the UK Parliament, says BBC home affairs correspondent Danny Shaw.
Bamber 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.
Moore killed four gay men for his sexual gratification in north Wales in 1995.