The children of three of Yorkshire Ripper Peter Sutcliffe's victims claim their mothers could have been killed by someone else who may still be at large.
Richard McCann fears a "copycat" killer could be at large
One of them, Richard McCann, made the claim after talking to a senior police authority member at the time of the killings and wants the case reopened.
Mr McCann, whose mother Wilma was killed in 1975, said two other children of Sutcliffe's victims were concerned.
But West Yorkshire Police say there is no evidence to support the claims.
Mr McCann, whose mother Wilma was Sutcliffe's first victim, told BBC Look North he recently spoke to Ron Warren, deputy chair of West Yorkshire Police Authority at the time of the killings.
He said he had studied press cuttings and was now "deeply concerned about Sutcliffe's confession".
Mr McCann said: "There is an element of doubt about this case and that frightens me.
"I had believed 100% that Sutcliffe carried out all the murders but now I'm concerned about a 'copycat' theory, after talking to people involved in the investigation."
He later contacted the children of two other victims - Patricia Atkinson and Irene Richardson - and said they are now equally concerned.
But retired detective Dick Holland, number two on the Ripper inquiry team, said there was absolutely nothing to support Mr McCann's fears.
Wilma McCann was the Ripper's first victim
In a statement to the BBC, West Yorkshire Police said: "These crimes were investigated at length by the force, resulting in Peter Sutcliffe being convicted.
"The investigation was also the subject of a lengthy and detailed enquiry by Sir Lawrence Byford.
"There is no new evidence to substantiate these claims."
Peter Sutcliffe was jailed in 1981 and given 20 life sentences for killing 13 women and attempting to kill seven more.
During the investigation valuable police resources were diverted after a hoaxer, who became known as Wearside Jack, pretended to be Sutcliffe.
Last week the hoaxer, alcoholic John Humble, from Sunderland, lost his appeal against an eight-year sentence for perverting the course of justice, after being arrested through DNA advances in 2005.
Humble's trial was told some of the Ripper's victims might not have died had he not diverted police with his hoax letters and tape.