Naomi Watts, Hollywood's Female Star of Tomorrow

Ghosts and goblins don't scare Naomi Watts— but other fears are creeping up on her.

The 34-year-old star of The Ring, opening this weekend, is one of the most sought-after actresses in Hollywood, after her critically acclaimed performance last year in Mulholland Drive.

Earlier this year, Watts was named the "Female Star of Tomorrow" at the ShoWest convention — the largest gathering for theater owners.

But as the star of a horror film, Watts is repeatedly asked about what spooks her — and it's nothing that goes bump in the night.

It's fame — or at least the demands of being in the spotlight.

"I'm particularly afraid of speaking in front of large crowds and red carpets," she says "Sometimes I get quite afraid of flying."

But if Watts is to become Hollywood's next big thing, she had better get used to it.

In The Ring Watts plays a Seattle reporter investigating a videotape that causes every person who watches it to die within seven days. It's a remake of a 1998 Japanese horror sensation.

At first cynical about the tape's paranormal powers, the cynical journalist ignores warnings not to view the tape.

But as soon as she does, she gets the same chilling phone call that all the other victims received — exactly seven days before they met a gruesome end.

David Lynch Precipitates ‘All Things’

"It's a genre film and you get all those moments that you get in a genre film," she says. "But you get a little bit more. I think it's more psychological and the character has her own personal journey to go through and I like it for that reason."

Watts acknowledged director David Lynch for putting her on the map by casting her in Mulholland Drive as a young starlet who becomes involved with an amnesic woman wandering in Los Angeles.

"He was the catalyst for everything," she says. "It did precipitate all things beyond that like this and the roles to come."

Born in Shoreham, England, and raised in Australia, Watts has been a working actress for 15 years in the film business, earning praise for her work in Wide Sargasso Sea, Gross Misconduct and Tank Girl, but remaining largely unknown to moviegoers.

All that's changing. In the upcoming months, you'll see her in Plots With a View, a quirky comedy about funeral homes, set in Wales, starring Christopher Walken.

You'll also see her co-starring with Heath Ledger in The Kelly Gang and with Kate Hudson, Glenn Close and Stockard Channing in Le Divorce.

She's currently working on 21 Grams with Sean Penn and Benicio Del Toro.

If success is now coming quickly, it's not a total surprise. Laurie MacDonald, one of the producers of The Ring, called Watts Hollywood's "longest-reigning new discovery."

Still, the thought of joining Hollywood's A-list is a bit daunting, she says.

"I realize I'm in a movie that's aiming to appeal to the masses," she says. "But you don't spend time thinking about that, and if you do you're in this for the wrong reason." ABCNEWS Radio contributed to this report.