“Saturday Night Life” cast member Jay Pharoah raised the issue of race among the show’s stars after the new members were added. (David Becker/Getty Images for Clear Channel)

During an often-glorious 38-year run, “Saturday Night Live” has featured some accomplished comic players of color: Eddie Murphy, Tim Meadows, Chris Rock, Tracy Morgan, Maya Rudolph, Kenan Thompson.

Is that enough diversity for a program that has come to define satire on American television?

The question has come up periodically since “SNL’s” earliest days. And it has come up again with the start of a new season, its 39th, last week. In another of its periodic resets of its ever-evolving cast, the show added six cast members this season — five of whom are white and male.

This development has elicited a rebuke of sorts from within. Jay Pharoah, who along with Thompson is one of two African Americans in the 16-member cast, told the Web site TheGrio this week that the NBC show should hire an African American woman. “They need to pay attention,” said Pharoah, who even promoted his own candidate, comedic actress Darmirra Brunson. “Why do I think she should be on the show? Because she’s black first of all, and she’s really talented. . . . And I believe they need to follow up with it like they said they were going to do last year.”

In the case of “SNL,” the cast tends to mirror its targeted audience, which is primarily young, white and male. But casting is often destiny. Performers frequently write sketches for themselves, and writers often write to the personas and characterization skills of the performers. That often has a strong racial component. When Rudolph returned to host the show in 2012 after leaving the cast five years earlier, for example, the difference was striking. She portrayed a series of black women — Maya Angelou, Beyoncé, Michelle Obama — who hadn’t been visible on the show in her absence.

Rudolph, who also memorably impersonated Whitney Houston, was a rare performer in more ways than one. In its first 38 years, “SNL” had 13 African American cast members, and only four them — Rudolph, Danitra Vance, Ellen Cleghorne and Yvonne Hudson — were women.

In 2008, the show passed over Thompson and other African American actors when it sought someone to portray Barack Obama. The role went to Fred Armisen, who is of Caucasian and Asian heritage and whose mother is Venezuelan. Armisen donned darker makeup for his portrayal, generating controversy as a result. Pharoah took over the role at the end of last season.

“SNL” has also turned its lack of black female representation into an inspired joke. In 2011, the show hilariously spoofed Beyoncé’s “Single Ladies” video by featuring three white guys (Justin Timberlake, Andy Samberg and Bobby Moynihan) as the high-heeled and leotarded backup dancers to the real Beyoncé.

“ ‘SNL’ has a history of including many hosts, musical guests and cast members with different backgrounds,” said Lindsay Shookus, the producer who oversees the show’s casting. “When we scout for the show, we always look for diverse voices and representation.”

A person close to the show said that Pharoah never mentioned Brunson before and that there was never a promise to add an African American woman to the cast.

The cast includes a performer of Hispanic-Tunisian descent (newcomer Noel Wells) and one of Persian heritage (Nasim Pedrad).

But nonwhite cast members are overwhelmingly the exception. Horatio Sanz and Armisen were the first and only Latinos in the cast until Wells arrived; Armisen and Pedrad are among the few Asian Americans ever to perform.

Some of this may reflect the pool of performers from which “SNL” recruits. Over the years, three improv companies — the Groundlings in Los Angeles, Second City in Chicago and Upright Citizens Brigade in New York — have supplied many of the show’s writers and actors. And those farm teams are often no more diverse: The Groundlings’ main cast of 30, for example, is all white, as is its secondary cast of 10.

“I think any [TV] producer will tell you that they would like a bigger pool to draw from,” Second City’s chief executive, Andrew Alexander, told Salon.com last month. “I think we’re just a reflection, so I assume that people who are producing television shows do wish there was a larger pool to draw from.”

The perceived whiteness of “SNL” has provided an opening for ­sketch-comedy programs that are more frankly racial, both in cast and in content, such as “In Living Color,” “Mad TV” “Chappelle’s Show” and Comedy Central’s current mini-hit “Key and Peele.” (K&P’s Jordan Peele recently said he auditioned for and was offered a role on “SNL” in 2008 but couldn’t get out of his contract at “Mad TV.”)

Ron Becker, an associate professor of media at Miami University in Ohio, says “SNL” may be somewhat out of step with an increasingly diverse American population, but it’s not out of step with its audience. It’s simply set up to serve the comic “sensibility” that young people — especially young white people — enjoy.

“The audience [for ‘SNL’] is implicated in this,” says Becker, the co-editor of “Saturday Night Live and American TV,” a new book of essays about the show. “If critics think segregation is a problem on the show, it’s also a problem with viewers. We tend to seek out the comedy that speaks to our sense of what’s funny, however we define that. We don’t seek out comedy that’s not for us.”

Becker points out that minority performers have far more opportunity to develop a following these days than when “SNL” began in 1975. Thanks to a fragmented media landscape, “you can speak to your audience on BET, on Comedy Central or narrow-cast through venues” on the Internet.

And is that kind of comedy segregation such a bad thing?

Actually, says Becker, it might be. “I would argue that it’s good for the social processes of our society if we have more material that reflects an integrated sensibility. In some small way, it might help us offset the kinds of polarization and self-segregation” that American society faces.