John Docherty, 49, also claims that at the time he is alleged to have stripped and strangled Elaine Doyle, 16, in a lane in Greenock he was at home with his parents, who are no longer alive.
Docherty, now of Dunoon, appeared at the High Court in Edinburgh at the start of his trial.
He pleads not guilty to a murder charge which alleges that on June 2, 1986, in a lane near Elaine Doyle's home in Ardgowan Street, Greenock, he seized her by the hair, struck her on the head and either removed or compelled her to remove her clothing.
The charge goes on to allege that Docherty forced Elaine to the ground, pushed her face into the ground, sat or knelt on the teenager then placed a ligature round her neck and strangled her.
Docherty also denies stealing a handbag from Ardgowan Street on the same date.
He further denies a charge of attacking another woman, Linda Hargie, on various occasions between 1990 and 1995 at an address in Anne Street, Greenock by seizing her and pushing her and punching her on the head.
As the trial began, the jury heard that defence QC Donald Findlay had given the court notice of Docherty's alibi. Another document lodged by the defence stated that Docherty denied murder and theft and blamed the crime on "person or persons unknown."
The so-called special defence of incrimination claimed the culprit might be among a list of names taken from files of the police investigation into the alleged murder and 41 names were read to the jury.
The jury then heard that a post mortem carried out on Elaine concluded that the cause of her death was "asphyxia due to strangulation by ligature."
The trial continues on Monday.