Relatives of soldiers killed fighting in Iraq today began the latest phase of their fight for the right to launch damages claims against the Government.
Families want to sue for negligence and to make claims under human rights legislation.
The Supreme Court began hearing arguments from lawyers representing relatives and counter-arguments from the Ministry of Defence (MoD) at a hearing in London.
Judges in the Court of Appeal and in the High Court have already considered the issues.
In October 2012, appeal judges said relatives could bring negligence claims but not claims under human rights legislation
In June 2011, a High Court judge had come to the same conclusions.
A panel of seven Supreme Court justices is expected to analyse arguments over the next four days.
Lawyers today began by outlining arguments relating to human rights legislation and are due to debate negligence issues later in the week.
Justices are expected to reserve judgment and deliver a ruling later in the year.
If given the go-ahead by the Supreme Court, relatives would be entitled to launch damages claims in the High Court.