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Kidnap survivor Jaycee Dugard says she will remain in hiding until her kids are old enough to understand

Kidnapping survivor Jaycee Dugard made her first public appearance over the weekend at a star-studded New York awards ceremony, but she plans to remain in hiding until her daughters are mature enough to understand what happened to them, she said in a recent interview.

Dugard, 31, and her two children, ages 14 and 17, have been living at an undisclosed California location since being found by authorities in 2009 - 18 years after she was abducted from a South Lake Tahoe bus stop.

She was held by Phillip and Nancy Garrido in their Antioch backyard, where she gave birth to two children conceived by rape.

In an interview that aired Tuesday night, Dugard told ABC News that she's spent the last three years healing and experiencing life with her family.

"I want my girls to have a normal life as much as possible," she told ABC News' Diane Sawyer. "I feel like on some things I have to do it a little bit differently ... not be recognized ... for their sake.

"I think in time as they get older, they'll know how to deal with it better, and that would be the time that we would come out," she said.

Dugard has been working to build the JAYC Foundation, which aims to support families dealing with abduction and other tragedies. She wrote a best-selling memoir last year, "A Stolen Life," which recounts her years in captivity.

Phillip Garrido is serving a 431-year prison sentence, and Nancy Garrido is serving 36 years to life, after both struck plea deals on kidnapping and rape charges. The state of California paid Dugard a $20 million settlement under which officials acknowledged repeated mistakes were made by parole agents responsible for monitoring Phillip Garrido, who was a convicted rapist.

Dugard describes years of captivity

Sawyer asked Dugard if either of the Garridos had tried to contact her. "No, not at all, which is fine with me," Dugard said.

Sawyer then asked Dugard if she has days when she doesn't think about what happened to her.

Dugard replied, "Oh, sure. It's not with me every day."

Asked if anyone had caught her eye romantically, Dugard said, "No, no, I just, I can't go there yet," Dugard said. "It's too soon."

July 7, 2011: Jaycee Dugard, the California woman who spent 18 years in captivity after being snatched from a street as a 11-year-old, is now revealing her horrific ordeal in an upcoming memoir. NBC's Aditi Roy reports.

Dugard was honored Friday at an awards ceremony held by fashion designer and humanitarian Diane von Furstenberg. She was introduced at the ceremony by Oprah Winfrey, another honoree of the night.

"Jaycee Dugard, I am so proud of you, your courage, your ability to press onward toward the future and toward a more victorious life for yourself and for using your courage, your strength, and your power to show the world that you care," Winfrey said.

During her first trip to New York, Dugard told Sawyer that she took in a Broadway play, admired the skyscrapers and enjoyed walking down the street among the crowds to get pizza.

"Just being free to do what I want to do, when I want to do it," she said. "That's the whole learning process to, to know that you can."