LOS ANGELES-Watch any classic Western, and you’ll see cowboys battling outlaws, fighting in bars, chewing tobacco and romancing women. But you wouldn’t expect them to have sex-at least not with each other.

Academy Award-winning director Ang Lee radically challenges this macho stereotype with his new film, Brokeback Mountain, a tale of two cowboys who fall in love.

Based on a short story by Pulitizer Prize-winner Annie Proulx, the film follows Jack Twist (Jake Gyllenhaal) and Ennis Del Mar (Heath Ledger), two young ranch hands hired to work as sheepherders on Wyoming’s Brokeback Mountain in the summer of 1963. They hardly speak to each other at first, but with time-and some alcohol-they unexpectedly develop an intense physical and emotional relationship.

After their seasonal stint in the wilderness, the two men part ways. Ennis returns to the nearby town to marry his longtime sweetheart, Alma (Michelle Williams), and Jack tries to break into the rodeo scene in his home state of Texas, where he meets and marries Lureen (Anne Hathaway), a rebellious heiress. The men start families and lose contact for four years, but when Jack sends his former lover a postcard, the two begin taking periodic “fishing trips” to Brokeback Mountain and start their relationship anew. Jack repeatedly proposes that the two live together, but Ennis, aware of the taboos and dangers of being openly gay, refuses.

“It feels like one of those great myths that has never been told,” Gyllenhaal says.

When the project was announced, many hastened to label it “a gay cowboy movie,” a description Lee hates. But Lee, who also directed Crouching Tiger, Hidden Dragon and Sense and Sensibility, says superficial opinions are sure to change when audiences see the film, which is due in theaters Dec. 9. Critics at the Venice Film Festival, where the film won the top prize, approached Lee and Gyllenhaal to express their surprise at the story’s depth. “The best way to respond (to the “gay cowboy” label) is to invite them to see the movie,” Lee says. “People stopped calling it a gay cowboy movie and started calling it a love story.”

Even Gyllenhaal admits that he initially was skeptical about working on the film. But he says he has overcome his fear of playing gay characters. “At first I wanted nothing to do with it,” says Gyllenhaal. “But I’ve grown, just as we all have grown.”

Gyllenhaal and Ledger’s characters aren’t typically found in Hollywood films. Lee acknowledges that he could have used gay actors, who might have had more empathy for the characters, but he believes he made the right choice. “I have to go with the best actor possible. Their disposition has to feed the character. I don’t ask people if they’re gay-they just have to be best for the movie. I presume you’re straight,” he says with a laugh, turning to Gyllenhaal.

Lee says the lead actors, nonetheless, were brave for taking their roles, but Gyllenhaal says locking lips with Ledger wasn’t as difficult as it may seem. “There are women I’ve done love scenes with that I’m not attracted to,” he says. “We’re all human beings. We all have lips.”

Gyllenhaal also expressed apathy when asked how his conservative fans will respond to his character. He says he chooses challenging, interesting roles-and maintains Brokeback Mountain is sure to satisfy some of his fans. “I’ve been told that I have a faithful gay audience,” he says. “I hope people respect the choices I make. My base isn’t about trying to appease a male audience, a female audience, a gay audience or a straight audience.”

Some critics have predicted that Brokeback Mountain will compete with Bennett Miller’s Capote for the best-picture Oscar, but Lee stresses that awards don’t matter. “I don’t think about how I want to be remembered,” Lee says. “I feel lucky. (My movies) are like my kids. I don’t judge them.”

Gay rights activists are heralding the movie as a breakthrough because it avoids typical media stereotypes. Gay characters-such as those in Mean Girls, My Best Friend’s Wedding and NBC’s Will & Grace-often provide comic relief through exaggerated femininity, but Brokeback Mountain represents being gay as a universal and timeless experience.

“People who say it’s a gay cowboy movie think it’s like Blazing Saddles,” Lee says. “They’re not gunslingers. They’re realistic characters.”

With the continuing fight for same-sex marriage and gay rights, the film’s timing may seem significant, but Lee says he isn’t trying to persuade audiences to think differently about homosexuality. “It’s not calculated,” he says. “If it’s a love story, it can come out any time. But I can’t wait for the whole world to be ready.”

Gyllenhaal, however, says the film’s moving story undoubtedly will change a few minds.

“I think there are high expectations for it from the gay community, and there should be,” he says.