At the start of a new decade, anime’s two top directors are being delivered to Americans by one company. And, no, it’s neither Disney nor Netflix.

The relatively unheralded Gkids, which was spun off 11 years ago from the New York International Children’s Film Festival by founder and CEO Eric Beckman, has now become the chief North American distributor of films by Hayao Miyazaki and Makoto Shinkai.

On Dec. 16 and 18, as part of its ongoing Studio Ghibli Fest, an annual April-December screening series, Gkids will present Miyazaki’s late artistic partner Isao Takahata’s final film, “The Tale of the Princess Kaguya,” in theaters across North America. On Jan. 15, the company will release Shinkai’s “Weathering With You,” Japan’s highest grossing film of 2019, on 900 screens nationwide.

Gkids also has a stake in anime’s less family-friendly material, like the edgier Studio Trigger’s first feature, “Promare,” an apocalyptic sci-fi adventure that mixes 2D and 3D computer-generated graphics and is a fan favorite on social media. (“Promare” will next run in U.S. theaters on Dec. 8 and 10.)

But prospects weren’t always this rosy for the New York-based company.

Over lunch at the Line Hotel in Los Angeles, Beckman recounts the story of the big one that got away: Shinkai’s 2016 breakout hit, “Your Name.,” which went on to become one of the highest grossing Japanese films of all time in any genre, earning over $361 million worldwide, second only to Miyazaki’s Oscar-winner, “Spirited Away.” It is now being adapted into a live-action Hollywood feature by J.J. Abrams of “Star Wars” fame, and a separate remake is reportedly in the works in China, where the original made most of its money outside Japan.

“We got the initial pitch for ‘Your Name.’ from Toho,” Beckman explains, “and it was just a little one-sheet with a picture and a short, poorly written synopsis. They couldn’t show us anything else yet. There was nothing for us to evaluate, so we offered our bid based on the commercial results of Shinkai’s previous film” — which were respectable but hardly record-breaking.

A third of the way into a screening of the completed movie in the fall of 2016, Beckman started frantically texting industry colleagues, hoping there was some way Gkids could get involved in its U.S. marketing. He was too late.

“Yeah, I’m still kicking myself. But I think that film surprised everybody,” he says. “It was the first film in a long time — and I see a lot of movies — where at the end of it I just wanted to hit rewind and watch the whole thing again.”

Gkids gives U.S. audiences a chance to see and re-watch titles in theater chain cinemas, a setting most artists prefer. Miyazaki, for example, at first resisted even the VHS and DVD formats, and until this October, when Gkids brokered a deal for Studio Ghibli with WarnerMedia’s forthcoming HBO Max platform, declined all requests for streaming licenses.

“Ghibli’s thing about not allowing streaming had to do with respect for the genre,” says Steve Alpert, the studio’s former director of international affairs, who has written a book about his experiences in the anime business that will be published in English next spring.

“Miyazaki and Takahata were making films for the big screen, to be seen by an audience with a great sound system in a darkened theater, and with no pausing to take a phone call,” Alpert says. “So now internet speed and streaming quality have improved, OK. But the important thing is that Gkids continues to promote viewing the films in the theater, to be seen as the filmmakers wanted them to be seen.”

Takahata’s “The Tale of the Princess Kaguya,” originally released in Japan in 2013, is widely considered a tour de force of cinematic animation. Based on a traditional Japanese folktale, its visuals evoke classic handscroll paintings (emakimono) enlivened by dazzlingly kinetic CG effects.

The story, about an adopted celestial princess dismayed by life on earth, is told nearly as much through Ghibli composer Joe Hisaishi’s eclectic score as it is through dialogue, making professional theatrical sound an imperative for its full appreciation.

To anime scholar and author Susan Napier, a professor at Tufts University, the Gkids screenings of Takahata’s swan song in U.S. cinemas this month are a godsend.

“I’m thrilled,” she tells me from her home in Kyoto, where she is currently on sabbatical. “In my opinion, ‘Kaguya’ is the most beautiful and the most affecting of all Ghibli films of the 21st century. Not only does it touch on a variety of emotionally moving subjects — growing up, the love between parent and child, how we manage loss — but it does so using some of the most striking and beautiful animation I have ever seen.”

Napier also applauds the deal forged by Gkids to stream Ghibli’s back catalogue. As she, Beckman and Alpert point out, there are audience members today who have never visited a movie theater. While she was writing her latest book, “Miyazakiworld: A Life in Art,” Napier says she was repeatedly asked where Ghibli films could actually be seen.

“I used to say, ‘Buy the DVD,’ but this method no longer works. I was getting seriously alarmed that young people wouldn’t be able to see any of Miyazaki’s films or the other amazing movies from Ghibli.”

The responsibility of presenting major anime artists to Americans keeps Beckman up at night. “I lose sleep because I don’t want to f—- it up,” he says. But he believes that the Japanese art form has now permeated world cinema. Its visual and narrative tropes, however broad in range, are intimately recognizable to generations in the U.S. And Gkids is betting that won’t change any time soon.

Roland Kelts is the author of “Japanamerica: How Japanese Pop Culture has Invaded the U.S.” and is a visiting lecturer at Waseda University.