NEW YORK — Even though Linda Ellerbee has addressed many tough topics with young audiences before, it took a decade before Nickelodeon approved her idea of a “Nick News” episode where children with terminal illnesses talk about their lives.

Her show, “Before I Go ... Living With Dying,” airs on the children’s network at 8 p.m. Sunday. The four featured children who are incurably ill address losing friends, fears for themselves and others, and their changed outlook on life.

Ellerbee, who has been making “Nick News” shows for 24 years, said she began pitching the idea 10 years ago after she worked as a hospice volunteer and came into contact with some dying children.

“I felt that it was an important show, not because half the kids in America are dying — they’re not — but because children have many questions about this,” she said. “It’s such an unknown to them.”

Eventually, she said about network executives, “I think I just wore ’em down.”

David Bittler, Nickelodeon spokesman, said the network worked hard with Ellerbee to make sure the program wasn’t scary or too sad but was ultimately uplifting. “We produced the special once we felt we got it absolutely right, and we are very proud of this episode,” he said.

Rhett, one of the youngsters profiled, was successfully treated for brain cancer but learned eight months later that it had returned. His mother had to tell him that he could not be cured and that it was up to the 13-year-old to decide whether to keep going with treatments. He shut it down, tired of being poked and prodded.

He’s pictured riding on a four-wheeler outside his Missouri home, saying that when he’s riding he doesn’t feel he has cancer. He said that life had more meaning to him than it did before he had cancer.

Nohemy, a 15-year-old brain cancer patient from near Los Angeles, is planning her funeral; she wants uplifting music and people wearing clothes with her favorite color, blue. And she worries about her parents.

The show’s candidness is typical of more than 150 such programs that Ellerbee has made for Nick through the years. She was nominated for a prime-time Emmy for a recent episode about middle and high school students coming out as gay or lesbian.