A woman who walked into a police station claiming she was kidnapped 18 years ago is likely to be telling the truth, police said last night. US authorities said the alleged kidnapper fathered two children with Jaycee Lee Dugard, now 29.

A woman who walked in to a police station 18 years after she was abducted had been kept in isolation in a ramshackle back garden, police said.

US authorities said the alleged kidnapper fathered two children with Jaycee Lee Dugard who amazingly emerged nearly two decades after she was snatched from a bus stop when she was 11.

Jaycee and the children, aged 11 and 15, were kept in sheds, tents and outbuildings at a remote house in Antioch, California.

The girl, as she was then, was snatched by two people in a car from a bus stop outside her home in 1991.

Police said they are "99% certain" the person who walked into Concord police station in California this week, 18 years after her disappearance, is Jaycee.

Speaking at a press conference, a spokesman for the El Dorado Sheriff's Department said two people were arrested on suspicion of kidnapping and other offences. They were named as Phillip and Nancy Garrido.

The new details came as authorities provided more information about the saga of Jaycee.

El Dorado County Undersheriff Fred Kollar said the woman spent most of her time in sheds and outbuildings to isolate her from the world.

"None of the children have ever been to school, they've never been to a doctor," said Mr Kollar. "They were kept in complete isolation in this compound, if you will."

There was electricity from electrical cords, rudimentary outhouse, rudimentary shower, "as if you were camping", he said.

Prison officials said Garrido later admitted the kidnapping after meeting with his parole officer.

He brought Dugard and the two children, ages 11 and 15, to the meeting.

The woman's family has been contacted and were last night in the process of arranging a meeting, said Lieutenant Les Lovell of the El Dorado Sheriff's Department, who was a detective assigned to help investigate the kidnapping in 1991.

"We are very confident at this point in time that it is her," he said.

Jimmie Lee, a spokesman for the Contra Costa County Sheriff's Department, said the two suspects were being held for investigation of several charges, including kidnapping.

Law enforcement sources said authorities were also searching a home.

Dugard's stepfather, Carl Probyn, said it was like winning the lottery.

"To have this happen where we get her back alive, and where she remembers things from the past, and to have people in custody is a triple win," he said.

Witnesses reported that a vehicle with two people drove up to Jaycee and abducted her while her stepfather was watching on June 10, 1991.

In reports, the girl's stepfather said he heard Jaycee scream then jumped on a bicycle and pedalled after the car in a failed effort to follow it up a hill.

He then turned around and screamed at neighbours to call the police.

The case attracted national attention at the time and was featured on TV's America's Most Wanted.

Mr Probyn said his wife, Terry, had spoken with the woman by phone.

He said the mother and their 19-year-old daughter were flying from their Southern California home to meet her in Northern California.

The story has echoes of the Josef Fritzl case. He was the 73-year-old Austrian who led a seemingly respectable life as a married man of seven children but who created a second, secret family following the multiple rape of one his daughters.

Fritzl lured his daughter into the cellar of the family home in 1984 where she remained for 24 years.

She gave birth to seven children, and Fritzl and his wife adopted or fostered three of them. Three other children, aged between five and 19, languished with their mother in three soundproof and windowless chambers, which were secured with electric locks and a remote control door. A seventh child died during birth, with Fritzl burning the remains.

Fritzl's secret was eventually uncovered in April 2008, when his daughter's eldest child became seriously ill. She persuaded Fritzl to take the girl to hospital, where staff contacted the police and the case unfolded.

Fritzl will spend his life in jail after being found guilty of rape, incest, murder and enslavement.