Anyone watching HBO’s ongoing miniseries “House of Saddam” surely must be struck by the lead actor’s resemblance to the late Iraqi dictator. Me? I was struck by something else: his Israeli accent. “Why does Saddam Hussein sound like my old grocer in Jerusalem?” I called out before checking the movie credits online. (Yes, an Israeli, but no, not my grocer.)

The post-9/11 era might be Hollywood’s Arab moment. But Israeli actors seem to be reaping the benefit, getting many of the best parts. Take Yigal Naor. Before portraying Saddam Hussein, the stout actor from Tel Aviv played Iraqi Ahmed Chalabi in “10 Days to War,” an Arab interrogator in the Hollywood film “Rendition” and a Palestinian militant in Steven Spielberg’s “Munich.” One of his costars in “House of Saddam” is Israeli Uri Gavriel, who portrays the depraved Chemical Ali. Gavriel also played a Saudi terrorist in “The Kingdom.”

The cultural crossover has a long history and has made a few Israelis regulars on the Hollywood character-actor circuit. Sasson Gabai says his run began with “The Impossible Spy,” a 1987 British film in which he played Syria’s defense minister. Since then, he has portrayed Arabs or Muslims in at least 10 films, most notably “Rambo III.” (He was Sylvester Stallone’s Afghan guide.) “It’s probably a combination of my Mediterranean look and my acting skills,” he says. Even Chaim Topol, who played Tevye in “Fiddler on the Roof” in the West End, has an Arab role to his credit: in the 1966 Kirk Douglas war drama “Cast a Giant Shadow.”

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Israeli actors are often preferred, some in the industry say, because their English tends to be good and their acting style is Western—as opposed to the more florid, theatrical technique popular in Arab drama. “It’s hard to find good actors anywhere,” says Avy Kaufman, a New York casting agent. “Israel happens to have some phenomenal ones.” In terms of technique, the crossover is not much of a stretch. Many Israeli actors grew up hearing Arabic and know something about the culture.

Certainly, plenty of Arabs are getting Arab roles. The Egyptian actor Amr Waked is riveting as Saddam’s brother-in-law in the HBO series, and he also had a good role in “Syriana.” Often, however, Arab characters in Hollywood films are terrorists—and many Arab performers won’t take those parts. According to Jack Shaheen, whose book “Reel Bad Arabs” chronicles the history of Arab stereotyping in U.S. cinema, nuanced roles for Arabs are rare. “I don’t believe casting directors think of Arabs in any other way except as playing terrorists or villains,” he says. But Alon Aboutboul, an Israeli actor who plays Al-Saleem in the recent thriller “Body of Lies,” says there’s a universalism in the anger and alienation of the characters he portrays. “I don’t think of playing a terrorist,” he says. “I think of someone who’s idealistic and believes passionately in what he’s doing.” Oscar nominee Shohreh Aghdoshloo, who is a star in her native Iran, plays Saddam’s wife in the HBO series and once played a terrorist on “24.”

Still, moviegoers across the Arab world must find it unsettling to see themselves so often depicted by their enemies. Arab conspiracy theorists, already convinced that Israel engineered the war on Iraq, must view “House of Saddam” as further evidence. As for my old grocer, he might be wasting his time. He could be a movie star.