Curtis Howard, 27, from Boston, Massachusetts, met Catherine Ayling when she and other students from Crewe and Alsager College, in Cheshire, went on an exchange visit to the Bridgewater State College, near Boston.
She was not attracted to him but he became so obsessed with her that he described her as his fiancee.
When she returned to England in 1989, he followed. He was sent back to America but returned using a false passport, and, after stabbing her more than a dozen times and cutting her throat, left her body in the boot of a hire car at Gatwick airport and fled.
An unwitting witness saw the attack in May 1991 in her college car park but thought the couple were engaged in 'horseplay'.
Howard, who was extradited from the US to face trial, denied murder but admitted manslaughter on the grounds of diminished responsibility.
Psychiatrists diagnosed him as a paranoid psychotic with a serious mental illness.
Accepting his plea at Hove Crown Court, Mr Justice Hidden adjourned the hearing case to 22 July 22 for reports.
The judge said a proper sentence might be long imprisonment or committal to a mental hospital.
Relatives of Catherine called for Howard never to be released. Her sister Teresa, 29, said: 'He should never in a million years be allowed out. Just put him away and throw away the key.'
Camden Pratt QC, for the prosecution, said that in August 1989 Catherine had gone on the one-year exchange visit to the US and Howard's interest in her was obvious.
Although Catherine always spoke to Howard, she was not attracted to him and had no sexual relations with him, Mr Pratt said. In December 1989 Catherine returned to Britain when her father died and Howard wrote and sent her an expensive leather jacket and money, although she did nothing to encourage him.
In June 1990, Howard came to Britain and Catherine's sister Sylvia found that her home in Littlehampton, West Sussex, had been broken into. A mattress and pillow had been slashed with a knife and on the bed she found a note reading: 'Catherine Ayling, you will burn in hell.'
On a door was scratched 'Catherine is dead' and on another there was a reverse swastika sign.
Howard admitted burglary and was returned to America, although not technically deported, Mr Pratt said.
Howard managed to persuade a friend, Dwayne Williams, to have a photograph taken with his glasses on and to apply for a passport. It was as Dwayne Williams that Howard regained entry to the UK. He made his way to Alsager, where he booked into a hotel and hired a car.
Then he attacked Catherine and drove to Gatwick airport. He left the body and the knife in the bloodstained boot, and flew home.
After returning to America, Howard confessed to a student adviser who alerted police when he read a report in the local paper of the abduction of Catherine. Howard was arrested by the FBI but contested extradition, claiming he would not receive a fair trial because of his race and press coverage.