Brendt Christensen obsessed with Ted Bundy and other serial killers.

An Illinois man accused of kidnapping and killing a graduate student from China two years ago was obsessed with Ted Bundy and other serial killers, a federal prosecutor said on Wednesday on the first day of the trial of the sensational case.

Brendt Christensen, 29, could face the death penalty if he is convicted in the June 2017 abduction and murder of Yingying Zhang, a 26-year-old student at the University of Illinois at Urbana-Champaign, 130 miles (210 km) south of Chicago. Zhang's body has never been found.

Christensen's defence lawyer acknowledged in his opening statement that his client killed Zhang but disputed the prosecution's version of events.

"You need to know who Brendt was and what he was going through - a downward spiral in his life," George Taseff told the jury as he sought to protect his client from the death penalty.

While the state of Illinois has outlawed capital punishment, a federal trial allowed prosecutors to seek the death penalty.

Christensen, who received a master's degree in physics from the university, has been charged with murder, kidnapping and lying to federal investigators. He has pleaded not guilty to all counts.

Christensen appeared in court wearing a blue shirt, hands cuffed behind his back. The trial is being held in Peoria, 90 miles (145 km) northwest of Champaign-Urbana.

Eugene Miller, an assistant U.S. attorney for central Illinois, said Christensen was obsessed with Bundy, who killed dozens of women in 1970s, and other serial killers.

"He kidnapped her, he murdered her, and he covered up the crime," Miller told the jury in his opening statement.

Before the crime he had researched how to abduct someone and purchased a very large duffel bag, he said. On the day of the murder, Christensen was looking for a victim when he found Zhang, who was small and had limited English, Miller said.

'HER BLOOD RAN DOWN THE WALL'

Christensen took Zhang to his apartment where she fought for her life as he hit her over the head with a baseball bat, raped her and stabbed her in the neck before cutting off her head, Miller said.

"Her blood ran down the wall," Miller said, as Zhang's relatives listened to an interpreter through headsets. "Thousands of miles away from her parents, alone with a stranger, she breathes her last breath."

Defence attorney Taseff told the jury he did not dispute that Christensen killed Zhang, which he called "a horrible crime." But he said he took "serious issue" with the government's account of events.

Taseff said Christensen had turned to alcohol and drugs as he struggled with an unhappy open marriage and a painful relationship with a girlfriend.

On the day of the killing, "he hits ground zero, rock bottom," Taseff said, after learning that his girlfriend was with another man that morning.

Christensen bought a bottle of rum from a liquor store at about 7:45 a.m., then drove around while drinking, Taseff said.

"At 2 o'clock in the afternoon," Taseff said, "he does the unthinkable."

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Zhang came to Illinois from China's southern Fujian province. She was studying photosynthesis and crop production at the university two months before she was reported missing on June 9, 2017.

Investigators were led to Christensen after surveillance cameras in Urbana recorded Zhang getting into a black car which authorities later traced to him, according to an arrest warrant affidavit filed with the court by an FBI agent.

Investigators alleged Christensen admitted to giving Zhang a ride, but said he dropped her off in a residential area a few blocks from where he picked her up.

Prosecutors showed video of Zhang getting into a black Saturn Astra that matched the car that Christensen drove. It was the last time she was seen alive.

Her then-boyfriend Xiaolin Hou told the court on Wednesday: "We will never give up hope to find her."