Dane who plays an immortal New York cop

Nikolaj Coster-Waldau, the star of Fox's

New Amsterdam

, doesn't have the standard resume for a prime-time actor.

Perhaps you caught him in Manden bag doren or Gode stromer. Both those films earned him nominations for a Robert. (The Robert Festival is Denmark's version of the Oscars.)

Coster-Waldau first spoke English as a child to NATO troops, trying out his rudimentary classroom vocabulary on the military personnel who were on maneuvers near his flyspeck of a village, Tybjerg.

"I found I could talk to the English soldiers," he says on the phone from New York. "And they would give me their food rations, which were really awful."

But once you've seen the actor, who looks like a cross between Viggo Mortensen and Denis Leary, there's no question he's leading-man material.

You just have to get past a hint of an accent. Which seems a little odd because in New Amsterdam (Mondays, 9 p.m.), he plays a modern-day cop who has been living in New York since 1642, thanks to a shaman's magic spell. You'd think he would sound like a local by now.

The dialogue is a work in progress. "I can hear the difference when I see the later episodes," he says. "It gets easier. Your ear adapts."

As a working European actor, Nikolaj Coster-Waldau (NICK-o-lie COST-er wal-DOW) has performed in numerous languages. And his English is far better than his French, a fact he was reminded of on a recent film shoot.

"The script was in French and I learned all my lines," he says. "I was working with this actress who was great, but she wanted to improvise. All I could do is look at her with great depth in my eyes."

According to David Manson, the executive producer of New Amsterdam, there's a reason that fake Americans are popping up on every network.

"The available pool of attractive, charming, irreverent male actors in their mid-to-late 30s has shrunk," Manson says. "It's a hard piece of casting. Most of the time, if they're that exciting, they've become movie stars.

"When I started doing series," says the TV veteran, "you were lucky if you got to go to New York to look for an actor. This year it's gone global. That's why you're seeing all these actors from England and Australia in prime time."

Coster-Waldau, 37, who auditioned for the part of John Amsterdam in London, is grateful that American television is going farther afield.

"When I first heard the premise - immortal cop - I thought, 'What is this about?' But as I read the script, I realized this can get really interesting," he says. "It has so much potential."

On the series, he plays a Rembrandt-era Dutch soldier in the New York settlement who saves the life of an Indian woman. In return, a medicine woman grants him eternal life. He will not age or die until he meets his one true love.

In the present, he is a Manhattan homicide cop, but over the centuries he has pursued every manner of profession: tinker, tailor, soldier, forger. We witness him pursuing his various vocations in flashbacks.

It was seeing Coster-Waldau in these historical set pieces that convinced Manson he had found the right actor for the role.

"He has a movie-star quality," says the producer. "Other actors seem boyish when you put them in period clothes. But there's a strength and a compelling masculinity to Nikolaj."

Talk about a hopeless romantic. When Amsterdam is not solving crimes, he's desperately pursuing "the one," even though finding her will result in his death.

"It's the classic story of a hero who has a goal," says Coster-Waldau, who adopted the hyphenate as a boy to hold onto both his parents' names when they divorced. "In order to achieve that goal, he has to go through adventures and tests and learn from those. He's lived very flawed lives in the past. We go back to all these events. On one level, for him to succeed in finding 'the one,' there are things he has to learn and things we have to learn about him."

Up to this point, Coster-Waldau has been traveling back and forth between New York and Copenhagen to spend time with his wife, Nukâka Motzfeldt, an actress from Greenland, and their two daughters. They've come over here three times as well.

If New Amsterdam is renewed for another season, that frequent-flier arrangement may change. "We would have to negotiate," he says. "It's not like my wife doesn't have a life and career of her own. It's not 'Dad has a job. Pack your bags. We're all going.' "

Either way, Coster-Waldau should be ecstatic, right? 60 Minutes recently reported that Danes are the happiest race on the planet.

The actor is a little skeptical about that finding. "Of course if you go further north in Scandinavia you find more gloom," he says. "The Danes are very content. But to say they're the happiest? No, I don't think so."