Although most fantasy relationships are harmless, there are times when the boundaries can be overstepped.

In one 1947 case cited by John L. Caughey in his book Imaginary Social Worlds, a 16-year-old Chicago schoolgirl named Ruth Steinhagen developed a crush on Chicago Cubs first baseman Eddie Waitkus. For two years she collected newspaper clippings about him and slept with his photograph under her pillow.

She fantasized about marrying him and when the Cubs traded Waitkus to the Philadelphia Phillies, she cried and told friends she could not live without him. In June 1949, Steinhagen arranged a meeting with Waitkus at a Chicago hotel where the Phillies were staying on a road trip. That afternoon she shot him in the stomach.

Waitkus survived and Steinhagen never stood trial. A Chicago court ruled that she was insane and committed her to a state mental hospital.

Two other cases cited by Caughey that are much more familiar:

* In December 1980, John Lennon was killed in front of his apartment building by Mark David Chapman, a fan who had used Lennon as a role model for 15 years.

* Four months later, John Hinckley, who was involved in an intense fantasy relationship with actress Jodie Foster, shot President Reagan in front of a Washington hotel.

In all three of these episodes the fantasy relationship was pointed to in court as evidence of mental abnormality.

Caughey points out, however, that Steinhagen's sister and friend were also engaged in fantasy relationships, that Chapman was only one of several fans who hung around Lennon's apartment building and that Hinckley was not the only young man sending love letters to Foster.

"The fantasy relationships they had to a media figure they hadn't met is used by psychiatrists, psychologists, the general public and the media as evidence that these people were insane," says Caughey.

But the University of Maryland anthropologist, who was sought out by the news media as an expert on fantasy relationships after Hinckley's assassination attempt, doesn't see it that way.

"The relationships they had until they decided to shoot . . . that kind of relationship, or something very like it, is extremely common in American society. Why these three relationships ended in violence is still unclear -- unstable people may have as much difficulty handling imaginary relationships as they do real relationships."

While it is abnormal for a fantasy to evolve into violence, "If you look at popular figures in our society," says Caughey, "their fame depends on people having a fantasy relationship with them. Brooke Shields, the Beatles, Michael Jackson: their status, their livelihood, their position depends on people devoting some kind of concern to them. One girl I interviewed said it was abnormal not to be involved with the Beatles at the time she was growing up."

Fantasy relationships become abnormal and approach pathology if, Caughey says, "the person is beginning to deal with the relationship in an antisocial way, if they think they should resolve it by some kind of violence."

Other clues are when the individual "feels uncomfortable with the relationship -- if there is subjective distress -- and the extent to which it interferes with a person's ability to carry on ordinary social relationships" with his family, friends and acquaintances.