Paul Whitters (15) died 10 days after he was hit on the head by a plastic bullet fired by an RUC constable on April 15, 1981 in Derry.
Julie Livingstone, a 14-year-old schoolgirl, was shot by a British soldier in west Belfast.
Their families wrote to the British Secretary of State Karen Bradley earlier this year after the Derry-based Pat Finucane Centre discovered that separate files under the names of Paul and Julie were to remain closed for decades.
Paul’s mother Helen Whitters and Robin Livingstone, brother of Julie, met Karen Bradley and her team of legal advisers to request the release of the files.
Afterwards, Mrs Whitters said: “The Secretary of State can’t tell us why the files are closed because the NIO has marked the files secret and because they are secret they claim not to know why they have marked them secret.
“The circular stupidity of this argument has left us speechless. This is about my son who was shot at almost point blank range at 15 years of age and about the cruel death at 14 of Julie Livingstone. They were just children.”
Paul O’Connor from the Pat Finucane Centre described the meeting with Mrs Bradley as “bizarre and deeply unsatisfactory”.
He said: “The families were told that there is nothing the Secretary of State can do to intervene and release the files to the families without the families engaging in a process of seeking the files under a Freedom of Information request, as the files are the property of the National Archives at Kew, London, and no longer anything to do with her or her office.
“She agreed the files were NIO files, that they had been submitted to the National Archives and that on the recommendation of the NIO they were closed.
“We asked why they were closed and asked what was in the files and they told us, ‘We don’t know what is in the files because they are closed’.
“When we said it was the NIO who closed the files, they said, ‘Yes but that was some time ago. We don’t know what is in the files and we don’t know why they were closed’.
“We were also told that the files are no longer the property of the NIO but belong now to the National Archive so the NIO cannot request they are opened.
“This was truly bizarre and deeply unsatisfactory.”
The NIO made the file on Paul Whitters secret in 2011 and on Julie Livingstone in 2014, then sent the files to the National Archives.
Mr O’Connor added: “This scandal obviously points to a wider issue that files can be closed, for reasons unrecorded except in the broadest of terms, passed onto the National Archives, where they then can be kept secret, but releasing them, even to the bereaved families of children killed, is much harder than making them secret.
“The families have asked to see in writing the full legal framework in which these decisions have been made, continue to operate and to which the Secretary of State informs them that she cannot intervene to ensure that the files are released to the families.
“They will then consult to decide how to progress on this extraordinary vista of state impunity but both families have vowed they will not rest until they have this resolved.”