It is understood the 55-year-old is being questioned at Preston police station in relation to two allegations, one of rape and another of sexual assault, against two men, both believed to be in their late teens.
The men reportedly made the allegations and gave statements to police last week about the alleged attacks.
Police forensic teams were seen conducting a search of the property yesterday, with a number of items being removed for analysis.
The offences are alleged to have been committed at Evans's home some time between July 2009 and March 2013.
He was still in custody when the Sunday Herald went to print last night and it was unclear whether any charges would be brought.
Prime Minister David Cameron and Commons Speaker John Bercow have both been informed about the arrest.
Evans, who comes from Swansea and whose parents ran a newsagent, has been MP for the Tory safe seat of Ribble Valley since 1992.
He has held a number of front-bench posts for the Conservative Party and was promoted to deputy speaker in 2010. He had also served as vice-chairman of the Conservative party.
In December 2010, he came out as gay in a newspaper interview in which he said that he was fed up of "living a lie" and had decided to tell all when he was threatened with exposure by a former MP.
A spokesman for Lancashire Police said: "A 55-year-old man from Pendleton in Lancashire has today, Saturday, 4 May 2013, been arrested by Lancashire Constabulary on suspicion of rape and sexual assault.
"The man will be interviewed at a police station in Lancashire during the course of the day.
"The offences are alleged to have been committed in Pendleton between July 2009 and March 2013.
"We take all allegations of a sexual nature extremely seriously.
"As a constabulary, we are committed to investigating sexual offences sensitively but robustly.
"We would encourage anyone who has experienced sexual abuse, or who has information about it, to have the confidence to report it to us knowing that we will take it seriously, deal with it sensitively, and investigate it thoroughly."
Neighbours were reportedly stunned by news of the MP's arrest.
One neighbour, who did not wish to be named, said: "It's shocking. I've known him for 12 years, ever since I moved here.
"He's always been such a nice neighbour. There have been lots of police cars coming and going, which is not something that we ever see here.
"The thought of him being arrested for rape is truly shocking. He's always seemed so pleasant."
ANOTHER woman who lives opposite Evans added: "I'm stunned. I don't know him well but I know he's the Deputy Speaker.
"I say hello and wave whenever I see him. I can't believe it."
Evans is said to be "popular and well-liked" among colleagues, with Whitehall sources reported last night as saying the arrest had come as a "total shock".
One source was quoted as saying: "The two men went to police claiming that Nigel had attacked them.
"It came as a bolt from the blue when police turned up at his door yesterday morning and arrested him."
Despite his own sexuality, Evans has had a mixed track record in parliament on gay-rights issues.
In 1998, he voted against lowering the age of gay consent from 18 to 16, but changed his mind two years later and voted in favour of the measure – which became law in 2001.
The MP was also absent from a vote in 2001 which paved the way for civil partnerships.
However, he backed the reform in 2004 following an agreed party line laid down by then Tory leader Michael Howard.
Evans also abstained in a vote on gay adoption.
It was only in 2003 that Evans became more active in the fight for equal rights – voting for the repeal of Section 28, which banned local authorities from promoting homosexuality in a positive light.
The Conservative MP also began to attend events staged by the equal-rights group Stonewall, which led the campaign for same-sex equality.
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