Audience data for US cable channels takes two days to be released, but overnight data indicates the series drew what the US audience measurement agency Nielsen calls a "2.1" household rating.

That made the series the highest rating program on a cable channel in the US on Sunday night, when it premiered there.

Though there can be some variance, programs which have drawn a "2.1" household rating in the past have drawn approximately three million viewers.

On that basis, the numbers could be interpreted as solid. The trade publication Variety described them as "good, but not spectacular".

Actual audience numbers will be released on Wednesday, Sydney time.

Jenner is the father of four children from previous marriages, Burt, Cassandra, Brandon and Brody, as well as two from his marriage to the socialite Kris Jenner, Kendall and Kylie. During his marriage to Jenner, he was also the stepfather of her four children, Kourtney, Kim, Khloe and Rob Kardashian.

Kim Kardashian's husband, the rapper Kanye West, also appeared in the opening episode, drawing approval on social media for his reaction to Jenner's transformation.

West said that Jenner's journey was "one of the strongest things that have happened in our existence as human beings".

"You couldn't have been up against more ... you're a celebrity, you have every type of thing, and it was still like, f--k everybody, this is who I am," West said.

Jenner later praised West for his "open-mindedness".

"I love how he's helped Kim come to grips with what's going on," Jenner said.

The series premiered in the US to largely positive reviews, though many critics seemed to note some contrivance and manipulation in the narrative, and noted the awkwardness of cameo appearances from the Kardashian family.

"I Am Cait mimics typical reality TV by trying to force dramatic narratives onto day-to-day life ... and while spotting the fakeness was part of the fun of the Kardashians, here it verges on counterproductive," The Atlantic said.

Slate was equally blunt, calling it "a respectable TV show with noble motives that easily evades [our] worst anxieties for it. And in doing so, it slams into what I never, ever could have imagined for it: dullness."

Slate's Willa Paskin later told US public radio the series shows Jenner had "a lot of integrity", but noted: "It is kind of a boring television show."

The series does tease some conflict between Caitlyn Jenner and the Kardashians, with a trailer that includes a scene where Kim Kardashian admonishes Jenner for hurtful remarks about the family.

"You look amazing, it's your time, but you don't have to bash us on your way up," Kardashian says in the clip.