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Mr Rapp claims the incident happened when he was 14-years-old
Star Trek actor Anthony Rapp said Mr Spacey, who was 26 at the time, made the pass after befriending him in 1986, at a party.
In an interview, Mr Rapp said he was inspired to come forward after the Harvey Weinstein allegations.
He said it was not: “To simply air a grievance, but to try to shine another light on the decades of behaviour that have been allowed to continue because many people, including myself, being silent.
“I’m feeling really awake to the moment that we’re living in, and I’m hopeful that this can make a difference.”
Mr Rapp claims he attended the party on his own and he was the only non-adult there. He was reportedly watching TV in a bedroom when he realised there was no one left in the apartment.
He claims at that point Mr Spacey entered the bedroom, picked him up and climbed on top of him in a sexual advance.
Mr Rapp said: “My memory was that I thought, oh, everybody’s gone.
“Well, yeah, I should probably go home.
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Everything I wanted to say about my experience is in that article, and I have no further comment about it at this time.
— Anthony Rapp (@albinokid) 30 October 2017
“Spacey sort of stood in the doorway, kind of swaying. My impression when he came in the room was that he was drunk.”
Mr Rapp said Mr Spacey picked him up like “a groom picks up the bride over the threshold”.
Rapp told BuzzFeed News: “He was trying to seduce me.
“I don’t know if I would have used that language. But I was aware that he was trying to get with me sexually.”
But I don’t, like, squirm away initially, because I’m like, ‘What’s going on?’ And then he lays down on top of me.”
He said that after a short time he was able to “squirm” away.
Mr Rapp said he has not spoken with Spacey since the incident but he told the story to several friends and family over the years.
The Star Trek star said he met Spacey for the first time at a celebratory event being held amid the success of “Precious Sons”, which he starred in and “Long Day’s Journey into Night”, which was Spacey’s breakout role.
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The Star Trek star claims Mr Spacey picked him up like a “groom”
Before the incident in the bedroom, Mr Rapp said he and a 17-year-old friend was invited to a nightclub by Mr Spacey after meeting them at a second post-show celebration.
Mr Rapp said he was invited even though he “looked younger than 14”.
He added that he does not recall being offered alcohol by Mr Spacey and the night was “a fun night of talking and hanging out”.
Mr Rapp tweeted: “I came forward with my story, standing on the shoulders of the many courageous women and men who have been speaking out, to shine a light and hopefully make a difference, as they have done for me.
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Mr Spacey responded on Twitter and said he didn’t remember the incident
“Everything I wanted to say about my experience is in that article, and I have no further comment about it at this time.”
Kevin Spacey responded to the accusation in a statement on Twitter.
He said: “I have a lot of respect and admiration for Anthony Rapp as an actor. I’m beyond horrified to hear his story. I honestly do not remember the encounter, it would have been 30 years ago.
“But if I did behave then as he describes, I owe him the sincerest apology or what would have been deeply inappropriate drunken behaviour, and I am sorry for the feelings he describes having carried with him all these years.
“This story has encouraged me to address other things about my life.”