Hollywood no longer dominates box office in the third-largest market in the world.

A decade ago, foreign films released in Japan grabbed a 67% market share ($1.4 billion gross), but that percentage fell to 34.3% ($689 million) in 2012 — the fifth straight year foreign films failed to cross the 50% line.

Some swings in market share can be explained by the reign of blockbusters (the “Harry Potter” series pushed Hollywood’s share up, while anything by Japanese anime auteur Hayao Miyazaki sends foreign entries packing), but a downward trend that goes back to 2006, when Japanese films took a majority share (52.3%) after 21 years of foreign reign, goes deeper.

U.S.-based media consultant Geoffrey Bossiere doesn’t believe the current pendulum swing away from Hollywood is purely a matter of box office physics. Hollywood tentpole pics, he observes, are becoming ever-more oriented toward destruction, violence and loud soundtracks. Watching such films at last year’s CinemaCon, he saw little that would entice Japanese audiences. Bossiere adds that he is not anti-tentpole: “As long as they have a really moving or tragic storyline or a really unique concept, they can work in Japan,” he says.

One recent Hollywood film that has worked well is “Ted,” which has topped Hollywood live-action releases in Japan in 2013 with $42 million. Japanese audiences love cute, even if they get their cute from a vulgar, substance-abusing animated bear.

What has not worked, at least very well, are Hollywood films with elements that seemingly would appeal to the Japanese market, such as “Pacific Rim,” with its robots and monsters inspired by Japanese anime and tokusatsu (“special effects”) films; or “The Wolverine,” with its samurai-style swordplay. Each took about $10 million at the box office.

“Japanese don’t care as much as they used to about Hollywood films, even if they are ones shot in Japan,” says one U.S. studio marketing exec, who wished to remain anonymous. Another reason “Pacific Rim” and “The Wolverine” didn’t do well in Japan, said the exec, is that they were too narrowly targeted to young male audiences. “What we’d like to see are more family-oriented films,” the exec added. “Too many films coming out of Hollywood are rather dark and depressing — there’s not a lot that families can take their kids to.”

Noting the soft numbers for live-action Hollywood releases last summer — “The Lone Ranger” led the pack with a so-so $21 million — box office analyst Hiroo Otaka said that the inability of these films to surpass $30 million (a feat accomplished by both “The Avengers” and “The Amazing Spider-Man” in the summer of 2012) indicates the present limits of foreign films here.

One exception to Hollywood’s fade is Pixar’s “Monsters University,” whose $90 million B.O. total was second over the summer to that of Miyazaki’s latest animated offering, “The Wind Rises,” which is projected to finish near the $150 million mark. Pixar and Studio Ghibli, Otaka says, have built powerful brands in the Japanese market.

Pixar may be able to benefit from the absence of any more films from Miyazaki, who announced his retirement on Sept. 6. Can the U.S. studios bet the market will open up again without his movies — and absent blockbusters like the “Bayside Shakedown” series (which made more than $400 million in Japan, including almost $73 million from the fourth film, “The Final”)?

Although Otaka says the era of the Japanese megahit may be over, auds are unpredictable. Recent box office results underline the continuation of the trend toward local films: In the second week of October, Hirokazu Koreeda’s “Like Father, Like Son” topped the charts, with $21 million, while only three Hollywood pics made it into the top 10: “Despicable Me 2” ($16.8 million); “Elysium” ($6 million); and “The Wolverine” ($7.5 million).

But Hollywood sees the territory in a different light. A Japanese marketing executive for a Hollywood studio who wished to remain anonymous calls the market steady, pointing to the relatively constant share for live-action U.S. pics over the summer: 21% in 2010, 26% in 2012 and 25% in 2013. The outlier — 42% in 2011 — was due to B.O. from the last “Harry Potter” installment.

Eight live-action Hollywood pics made $10 million or more last summer, while only five did in 2012 — but total B.O. for these pics for the two periods was nearly identical, and that takes into account 3D upcharges, which are among the highest in the world in Tokyo at an average of $21.

In the meantime, those analyzing the Japanese market can wait for “Monsters Graduate School” or the next film by Studio Ghibli to skew the numbers once again.

(Pictured: “Like Father, Like Son,” Hirokazu Kore-eda’s take on family bonds, beat “Despicable Me 2” and “Elysium” at the Japanese box office.)