Two mothers of British servicemen killed in Iraq are challenging the government's refusal to hold an independent inquiry into the conflict.
Fusilier Gentle was killed by a roadside bomb in June 2004
Appeal judges have already told them they face "formidable hurdles" in establishing their case.
A QC for Rose Gentle and Beverley Clarke told the Court of Appeal they were proud of their sons but questioned the legality of the invasion.
The government's legal team will resist a full public inquiry.
Fusilier Gordon Gentle, from Glasgow, and Trooper David Clarke, of Staffordshire, were 19 when they were killed.
Human Rights breach
Ranbinder Singh QC said their deaths had left "grieving parents in whose minds there are real questions about the legality of the invasion of Iraq in March 2003".
He said their questions included the process which led to the invasion.
The families want the government to explain how 13 pages of advice from the attorney general on 7 March 2003 about the legality of the war was changed to one page by 17 March saying an invasion would be legal.
Mr Singh said: "We submit that it was at least reasonably arguable that there is a causal link between the assurance given by the attorney general and the deaths in question."
He also argued that the families were entitled to an independent inquiry under the principles of Article 2 of the European Convention on Human Rights, which protects the "right to life".
But QCs appearing for the prime minister, the defence secretary and the attorney general, said if that argument was accepted it would mark "a significant, constitutional shift".
Attorney General Lord Goldsmith has argued that the decision not to sanction a public inquiry was "entirely reasonable".
Rose Gentle was in court for the day's proceedings but illness in the family prevented Beverley Clarke from attending.
Outside court Mrs Gentle urged Tony Blair to order a full public inquiry, and she referred to a Commons vote in which a bid to get an inquiry failed.
"Why can't Tony Blair be man enough to stand up and say he will give an inquiry and stop a lot of court cases going ahead?" she said.
"What has he got to hide? Our boys are being killed day-by-day. If we do succeed in this case it will be a bonus.
"If we don't, we can say we tried and we fought for the boys and have got more backbone than the MPs who didn't stand up for them in last week's vote."
Last December, a High Court judge ruled they did not have a case to go to a full judicial review hearing.
But appeal judges have allowed their case to go forward.
The action is also being brought by two other parents - Peter Brierley, father of Lance Corporal Shaun Brierley, from West Yorkshire, and Susan Smith, mother of Private Phillip Hewett, of Tamworth in Staffordshire.
This latest challenge, which is expected to last three days, comes shortly after an attempt to force the government to hold an inquiry into the Iraq war failed in the Commons.
A motion for an immediate probe was opposed by a majority of 25 despite support from 12 rebel Labour MPs.
Prime Minister Tony Blair said he had not ruled out a retrospective inquiry.