David Leckey (11) and 14-year-old Jonathan Aven were last seen in east Belfast in September 1969.
The PSNI said their families have suffered “unimaginable pain” since they went missing.
They believe the boys may have got on the train to Bangor and have urged anyone who may have encountered them in any circumstances or location over the past 56 years to come forward to police.
They said the family of David, from Memel Street, had “no indication that he was unhappy or in trouble of any kind and didn’t think he would ever have left home” when he went missing.
Jonathan, from Sydenham Drive, was described by his father as a “happy little boy” who attended Ashfield Boys’ School, “which he seemed to like and appeared to be doing well at”.
“More than 50 years have now passed since both David and Jonathan went missing, their families have suffered over these years not knowing what happened to them on the day they left their home addresses,” a police spokesperson said.
“The pain and suffering of not knowing throughout the years must be unimaginable. Our thoughts very much remain with the families of both David and Jonathan at this time.
“This remains an open missing persons case with the circumstances around their disappearance still unexplained.
“Detectives will consider all investigative opportunities and follow all lines of inquiry as part of the review and will consider any potential criminal offences that may be linked to their disappearance.”
They added: “If anyone has any information in relation to the disappearance of David and Jonathan, we would ask them to contact Legacy Investigation Branch where all information will be assessed and considered by investigators.”
Acclaimed 2023 documentary Lost Boys: Belfast’s Missing Children linked their disappearances to members of a paedophile ring which allegedly operated with the knowledge of MI5 and involved some of its agents.
It also looked at possible links with the disappearances of Thomas Spence (11) and John Rodgers (13), who were last seen at a bus stop on the Falls Road, west Belfast, in 1974, and the murder of Brian McDermott (10), who was last seen at Ormeau Park on September 2, 1973.
His dismembered body was found a week later in bags found in the River Lagan. Police also recently issued a new appeal about the murder.
In Lost Boys a controversial loyalist pastor, Alan Campbell who died in 2017 aged 67, was linked to the disappearances of the four Belfast schoolboys and the murder.
The documentary also referenced a news report from 1980 which mentioned that RUC detectives investigating the sex abuse at the notorious Kincora Boys’ Home in east Belfast were also examining the files on the Aven and Leckey disappearances.
Missing boys David Leckey and Jonathan Aven
News in 90 Seconds – September 21st