Marv Films/Lionsgate

Chloë Moretz, 13, uses foul language in a violent, R-rated trailer for a new film.

Yet there they are, roaring out of the mouth of a cute little 11-year-old girl.

A trailer for the forthcoming film“Kick-Ass” that depicts the girl wielding a gun and using highly, highly profane language is igniting debate about how Hollywood advertises its R-rated films on the Web.

Movie marketers in recent years have increasingly relied on raunchy ads known as “red-band” trailers to stir interest in their films. While most trailers are approved for broad audiences by the Motion Picture Association of America, the red-labeled variety usually include nudity, profanity and other material deemed inappropriate for children. Many theaters refuse to run these trailers, but they are widely distributed online — and that is at the root of the current dust-up.

One R-rated trailer for the movie, about a teenage boy who tries to become a superhero, was released by Lionsgate in late December and has become a Web phenomenon. The trailer primarily focuses on Hit Girl, an 11-year-old sword- and gun-wielding vigilante played by Chloë Moretz (who just turned 13 in real life). Nicolas Cage plays her father, an equally menacing oddball named Big Daddy.

In the trailer Hit Girl salts her conversation with language so graphic that it would make a biker blanch; it’s well beyond the kind of garden- variety profanity that has seeped into mainstream culture. She then shoots a man in the face and uses a whip to kill another.

Lionsgate, which acquired the North American distribution rights to this independently produced film, released another red-band trailer on Friday. This one adds references to masturbation in the boy’s voice and has another cascade of under-age cursing.

In both instances Lionsgate complied with industry rules for red-band trailers. The Motion Picture Association of America, the trade organization that bestows ratings and regulates movie advertising, restricts release of these ads to sites that require viewers to pass an age-verification test, in which viewers 17 and older have to match their names, birthdays and ZIP codes against public records on file.

The problem is that the raunchy trailers pop up on sites without age restrictions almost instantaneously. Fans copy them to their own blogs and Facebook profiles and post them outside of YouTube’s so-called age gates. All movie trailers go viral, but the red-band ones speed across the Internet with an added velocity because of their “can you believe what they just said” nature.

“Studios hide behind the notion of an age requirement for these trailers, but it’s pure fiction,” said Nell Minow, a lawyer who reviews films for radio stations and Beliefnet.comunder the name Movie Mom. “It’s easy for kids to access, and that’s exactly how the industry wants it.”

Moreover, the severity of age policing varies, with some sites — including the Trailer Park section of MySpace, which had the red-band version as of Tuesday — seemingly leaving it to the honor system and asking for only an easily lied-about birth date. (A MySpace spokeswoman, Tracy Akelrud, said the site used other controls to detect under-age users. “If you are under 17, you will be blocked,” she said.)

The global nature of the Internet poses another challenge: foreign Web sites, which do not fall under control of the motion picture association, are easily reached through Google.

Red-band trailers had such a bad reputation in some studio circles that as recently as 2007, Warner Brothers wouldn’t even do them, saying it cost too much to make trailers for such a niche audience. But at the moment, one of the hottest trailers on the Web is a red-band variety for Warner’s “Cop-Out,” featuring a cursing 10-year-old. The Hollywood Reporter wrote about its “all new potty-mouthed flavor!”

Ms. Minow, who is also a shareholder activist and the daughter of Newton N. Minow, a former chairman of the Federal Communications Commission, has been stewing about red-band trailers for years, but the particularly graphic ones for “Kick-Ass” have brought her to a boil. She said she had lodged multiple complaints with the motion picture association in recent weeks. Other family advocacy groups — including one as far-flung as Australia — are rallying around her.

“These particular trailers are even worse than normal because they depict a child and so are more interesting to children,” Ms. Minow said. She is also upset that the movie showcases a child engaging in such behavior in the first place, adding, “Isn’t there a limit to what we can ask children to do on screen?” (Similar questions were raised in 1976 when a 13-year-old Jodie Foster played a teenage prostitute in “Taxi Driver.”)

The film at the center of the new controversy, directed by Matthew Vaughn, with a budget of around $35 million and set for release in the United States on April 16, is based on the popular — and equally violent — comic book series of the same title by Mark Millar. Mr. Vaughn’s company, Marv Films, and Plan B Entertainment, a company owned by Brad Pitt, financed the movie. Advance interest in the film is enormous, according to pre-release tracking surveys, and Hollywood widely expects it to be a hit.

The motion picture organization acknowledges the problem of “bleed” — the term the industry uses for marketing materials that spread beyond their specific target audience — but bristles at the notion that it could do more to protect children from inappropriate movie advertising.

“We devote enormous resources to making certain that kids don’t encounter these trailers,” said Marilyn Gordon, the organization’s senior vice president for advertising. “That said, we can’t scrub the entire Internet.”

She said the association proactively searched for sites that provide unrestricted access to red-band trailers and, working with studios, demanded their removal. Since the Hit Girl trailer was released in December, Ms. Gordon said the organization had found 86 sites providing unrestricted access. As of Monday, all but a few had removed the video. One of the remaining was out of the organization’s jurisdiction: a fan site in Eastern Europe.

Lionsgate, which gained notoriety as the studio behind the violent “Saw” franchise, in many ways prides itself on button-pushing marketing. But with this film, studio executives say they are simply using red-band trailers to educate moviegoers about exactly what awaits. Because of Motion Picture Association of America restrictions, the “green band” trailer approved for broad audiences features little swearing or sex references and depicts comparatively little violence.

In a statement the studio said, “It’s really important for people to know what kind of movie this is so they can make an appropriate decision about whether or not they want to see it.”