The abuse took place while the boys were living at Belmont House, in Baker Street, Stockport, Greater Manchester, in about 1989 and 1990.
The home, which was also known as Belmont Assessment Centre, has closed.
Police have made "extensive" inquiries and are now appealing for anyone who worked or lived at the home during that period to contact them.
Det Con Karen Wileman said: "People who were previously residents or members of staff at the home may have moved to different areas of the country, or even abroad.
"We are keen to speak to anyone who was involved with the home around the time the abuse took place."

Siale Angilau, 25, died in hospital after being shot several times by a US marshal in front of the jury at the new federal courthouse.
The FBI said he had rushed towards the witness with a pen in an "aggressive, threatening manner".
Angilau was the last of 17 accused gang members tried as part of a 2010 case.
The case included 29 counts, including assault, conspiracy, robbery and weapons offences.
Perry Cardwell, who was in the courtroom with his adult daughter, told the Associated Press news agency at least six shots were fired.
"It was kind of traumatising," Sara Jacobson, his daughter, said.
The witness on the stand at the time was not identified and was not injured.
He appeared to be in his mid-20s and was testifying about gang initiation, Mr Cardwell said.
US District Judge Tena Campbell declared a mistrial, writing in her order that members of the jury were visibly shaken and upset.
Angilau's lawyer declined to answer questions as he left the court on Monday. The accused had been transferred to federal custody last week after serving time in prison in Utah on other charges.
The new federal courthouse in Salt Lake City opened just a week ago. It was designed with several security features, including bulletproof glass in some areas and separate routes in and out for judges, prisoners and the public.
The building was closed for a while after the shooting but later reopened.

BBC Northern Ireland is planning to move from its premises at Broadcasting House on Ormeau Avenue.
The corporation has yet to decide on a site.
The council has set out its preferred options for the broadcaster in its regeneration and investment strategy.
It said lands to the rear of Belfast Central Library, a site north of Great Patrick Street or the stalled Royal Exchange development could all be suitable.
It has recommended that a working group involving the BBC, the council, the universities and other agencies should be formed.
The Ulster University is currently building a major extension to its Belfast campus on the northern edge of the city centre.
Adjacent streets are also due to be redeveloped as part of the Northside scheme.
The council strategy expresses hope that a major department store, such as John Lewis, will anchor the Royal Exchange development.
But it states that if the retail option is not possible the BBC "would be an obvious candidate" as an anchor tenant.
The BBC has previously been linked with a move to Titanic Quarter or as part of the redevelopment of Great Victoria Street station.
The council's strategy also contains details of its Â£19m city centre investment fund.
It could be used to make loan or equity funding to developments or for the council to buy development sites.
An appeal has been launched after two boys were sexually abused at a former care home.
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A man accused of robbery and assault was shot and killed in a Salt Lake City court after he lunged at a witness giving evidence.
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Belfast City Council has said a BBC relocation to a site beside the Ulster University campus would lead to a "comprehensive transformation" of that part of the city.