Three more women have come forward claiming Bill Cosby sexually assaulted them, as a lawyer challenged the veteran comic to let himself face legal action over decades-old alleged attacks.

The trio of women appeared at a Los Angeles press conference called by lawyer Gloria Allred, who urged Cosby to waive his right under the statute of limitations, which limits how long after the fact lawsuits can be filed.

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One of the three victims, Beth Ferrie, told how she had an extra-marital affair with Cosby in the 1980s.

Then a few weeks after she ended the relationship, he invited her to a show.

She drank a coffee he offered her and began to feel “dizzy”, she said.

Attorney Gloria Allred (2nd from L) speaks during a press conference with alleged victims of Bill Cosby; Chelan, Beth Ferrie and Helen Hayes, on December 3, 2014 in Los Angeles, California. Photo: Getty

“The next thing I knew, hours had passed. I woke up in the back of my car, alone, my clothes were a mess, my bra was undone and my car was in the alleyway behind the venue,” she said.

Later, having regained her senses, she went to confront him. Cosby said she had had too much to drink, but she denied drinking any alcohol.

“I believe that Mr Cosby drugged me and sexually assaulted me that night,” she said.

Another woman, Helen Hayes, said she met Cosby while attending a celebrity tennis tournament in California in 1973. At some point he approached her from behind and grabbed her breast, she said.

“His behaviour was like that of a predator,” she said.

A third alleged victim, identified as Chelan, said she met Cosby when she was 17. She was working at a hotel in Las Vegas, and Cosby called her to his room and said he would introduce her to a modelling agent.

“He laid next to me on the bed and began pinching my left nipple,” she said.

Allred said: “We challenge Mr Cosby to end this nightmare,” by waiving the statute of limitations for rape charges.

Cosby then “would have an opportunity to address these allegations in a court of law, and the victims and Mr. Cosby would have an opportunity to have a judge and a jury decide who should be believed,” she said.

Around 20 women have now accused the 77-year-old Emmy and Golden Globe winner of sexual assault and even rape in alleged incidents dating mostly from decades ago.

One alleged victim, 55-year-old Judy Huth, sued Cosby in Los Angeles Superior Court claiming sexual battery and infliction of emotional distress.

She says that at age 15 she and a friend, then 16, met Cosby on a film set and that he invited them to meet at a tennis club the following week.

Cosby is world famous for his role in The Cosby Show in the 1980s and 1990s.