A man described as a "sexual predator" has been found guilty of a 1979 murder and five attacks on other women.
Sally McGrath, 22, was found naked in a shallow grave in woodland near Peterborough, Cambridgeshire, in March 1980 after vanishing in July 1979.
Her killer could not be found despite a major police investigation.
Former soldier and builder Paul Taylor, 60, originally from Peterborough and now of Valentine Close, Fareham, Hampshire, was arrested last year following a cold case review.
At Chelmsford Crown Court, a jury found him guilty of murder following 23 hours of deliberation. He was found guilty of three counts of rape, one attempted rape and a serious sexual assault, which were all committed in the months leading up to Miss McGrath's murder.
Mr Justice Owen told Taylor: "You have finally been brought to justice and you will now serve life in prison." Taylor will be sentenced on Wednesday morning.
He commended Cambridgeshire Police detectives for solving the mystery, which officers at the time had failed to bring to court despite the force's biggest pre-Soham investigation. The force said it would now investigate possible further sex attacks committed by Taylor during the years he escaped justice.
Detective Superintendent Jeff Hill, who led the new investigation, said: "As a result of this inquiry, we have already considered what other offences may have been committed by Taylor. Given the nature of the offending, there is every chance that similar crimes have occurred that we just quite simply don't know about."
Taylor denied the charges, saying that all of the sexual incidents either did not happen or were consensual. He claimed there were many other people who could have killed Miss McGrath.
Opening the trial, prosecutor Karim Khalil told the court Taylor was married at the time of the 1979 offences. Describing Taylor as a "sexual predator", Mr Khalil added: "But if he did not have his own way, he had the capacity to become violent very quickly. He used this violence to force young women into submission or simply have his way with them."
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