He is charged with the shooting death of an old boyfriend and is a suspect in the fatal bludgeoning of another acquaintance. He is wanted for questioning in connection with the slashing and torture of a prominent Chicago tycoon who suffered, in the words of his 96-year-old mother, ““a worse death than Christ.’’ On Friday night, as Cunanan allegedly fled eastward, police suspect he struck again, murdering the caretaker of a cemetery in New Jersey with a single shot to the head. The evidence is circumstantial, the motive a mystery. But as the 27-year-old zigzagged across the country, a trail of clues, from a sandwich to a claw hammer covered with blood, was found in his wake.

In the gay bars of San Diego, the boisterous and eccentric Cunanan was known as the guy who would always pay the check and leave a big tip. He was vague about where the money came from, suggesting to some that it came from his ““rich Jewish family’’ (““Named Cunanan?’’ wondered a friend), and to others that his father owned land on the Riviera and a plantation in the Philippines. In late April Cunanan threw himself a farewell dinner (ostrich, trout and champagne) and announced that he was moving to San Francisco. The next day, according to police, he flew to Minneapolis to see Jeffrey Trail, a former navy lieutenant he had met in a San Diego bar. Trail agreed to meet Cunanan at a coffee shop, telling a friend he would catch up with him later. Trail never made his second appointment. While in Minneapolis, police say, Cunanan stayed with an ex-lover named David Madson, an architect. The night Trail disappeared, Madson’s neighbors heard angry shouts and loud thuds coming from his apartment.

Two days later, on April 29, Trail’s body was discovered in Madson’s apartment, wrapped in a rug; the bloody claw hammer was found nearby. Cunanan and Madson had disappeared. But on May 3 two fishermen stumbled across Madson’s body near a lake north of Minneapolis. Madson had two bullet holes in his back and one in his head from a .40-caliber pistol. Police later found an open box of .40-caliber shells in a bag that bore Cunanan’s name. Cunanan, they suspect, had killed Trail and then murdered Madson to eliminate him as a witness.

But where was Cunanan? Police say he was last spotted driving north - toward the lake - with Madson in his friend’s red Jeep Cherokee. On Sunday, May 4, Marilyn Miglin returned to her row house on the tony Gold Coast of Chicago’s North Side, wondering why her husband, real-estate developer Lee Miglin, had failed to meet her at the airport. The son of a coal miner, Miglin had always been fastidious, yet there were dirty dishes and a half-eaten ham sandwich in the kitchen, and some beard stubble in a bathroom sink. Marilyn Miglin called the police. In the garage, they found a blood-spattered chamber of horrors. Miglin’s body was riddled with shallow stab wounds. His head was wrapped in tape, with a breathing space under his nostrils. His throat had been slashed with a gardener’s bow saw. Police believe that he had been tortured - to make him divulge the whereabouts of cash or valuables? It’s possible that the killer surprised Miglin while the developer was eating the ham sandwich. Or perhaps the murderer, his dirty work done, had a snack and a shave and even spent the night.

Two days later police found Madson’s red Jeep Cherokee, collecting parking tickets, only 55 yards from Miglin’s row house. Miglin’s jade green Lexus was gone. Police could find no link between Cunanan and the Chicago tycoon. The Miglins were socialites and philanthropists; Marilyn Miglin was a successful perfume-and-cosmetics entrepreneur known as the Queen of Makeovers. Police wondered whether Cunanan might have known about Miglin through his son, Duke, an aspiring actor who lives in Los Angeles, but the younger Miglin says he never met Cunanan.

Last Wednesday and Thursday, police picked up fleeting signals from the cell phone in Miglin’s car - first in western Pennsylvania, then outside Philadelphia. On Friday night, the wife of the custodian at the Finn’s Point National Cemetery in southern New Jersey called the police after her husband, William Reese, 45, failed to come home. His body was found lying, with a bullet in the head, in the basement of his office. Miglin’s stolen Lexus was nearby. The killer had taken the caretaker’s red Chevy pickup and vanished. The FBI issued an all-points bulletin for Cunanan.

The suspect is at once as showy and shadowy as the trail he left behind. Cunanan, who often used an alias, was not quite the high roller he pretended to be. He lived in a small apartment in San Diego, and he owed $20,000 on one credit card, $5,000 on another. His mother lives in public housing in Eureka, Ill. His father, a stockbroker who is reportedly wanted for misappropriating funds in 1988, lives in the Philippines, or possibly under an assumed name on the West Coast. A close friend told NEWSWEEK that Cunanan had been ““kept’’ by wealthy gay lovers and dabbled in ““shady dealings,’’ including drugs. Minneapolis police suggested that Cunanan feared he had contracted AIDS and was determined to settle scores.

If Cunanan is held responsible for all these deaths, he may be remembered not so much as a serial murderer but as a ““spree killer.’’ Most serial killers are middle-aged males with jobs and outwardly normal lives. They methodically stalk their victims. Spree killers, by contrast, swing into action without warning. Rarely do they elude capture or death. ““They’re so high profile, killing at such velocity, that it’s hard to miss them,’’ says James Fox, dean of criminal justice at Northeastern University. ““They get a taste for murder, and they’re off.''

Cunanan has been careless about leaving clues, and he almost seems to be taunting police by racing across the country in flashy vehicles. His true motivations may never be known. ““The most likely way for this to end is, he’s going to commit suicide,’’ said Lt. Dale Barsness, head of the Minneapolis homicide unit. ““Whether he kills more people before that, I don’t know.''

The evidence is circumstantial but titillating. Police think that Andrew Cunanan may have left San Diego and begun a descent into darkness,possibly killing people in Minnesota,Illinois and New Jersey. A look at the events:

April 24:Andrew Cunanan,27,a high profile member of the area’s gay community,host a dinner,announcing he is leaving for San Francisco.

April 25:Cunanan flies to Minnesota,where he meets with David Madson,33,a former lover.

April 29:When Madson fails to show up for work,friends go to his home and find the body of Jeffrey Trail,a gulf-war veteran who once lived in San Diego. Trail,28,has been beaten to death. A bloodied hammer is found.

May 3:Madson,s body is found at an abandoned farm north of Minneapolis. He has been shot three times. His red jeep is reported stolen,and Cunanan is charged with second-degree murder.

May 4:The wife of wealthy real-estate magnate Lee Miglin comes home from a trip,finds her 72-year old husband missing and calls police. In the garage they discover Miglin"s body,wrapped in brown paper and plastic,his face covered with masking tape and his throat severly cut by a gardener’s bow saw. The philanthropist’s Lexus is missing.

May 6:Police find Madson’s Jeep illegally parked 50 yards from Miglin’s home.

may 8:Chicago authorities monitoring the cellular phone in Miglin’s Lexus inform Philadelphia police the phone has been nearby.

May 9:A caretaker at Finn’s Point National Cemetery is found dead,shot in the head. His pickup truck is missing,and Miglin’s Lexus is found abandoned at the scene.