It was the last day of February. Critics of TV violence were getting restless, Technically the Family Hour was dead, but the clamor was rising for more programs the family could watch together. It was a fine time for Fred Silverman, ABC programming honcho, to make his announcement.

"Family," he said, was renewed for next season - the first ABC show to get that vote of confidence. Attention must be paid to "Family," added Silverman, because it "reflects in such a positive light the basic values of a family unit as it copes with the real pressures of contemporary American life."

Spelling-Goldberg Productions supplies "Family" to ABC. Its other creations for ABC include "The Rookies," "S.W.A.T.," "Starsky and Hutch" and "Charlie's Angles."

A TV genre has arrived in commercial American terms - the prime-time family drama.For networks that are on the defensive about TV violence, it could come in handy.

Each network has one, First came "The Waltons" at CBS, then NBC's "Little House on the Prairie." Even PBS is covering some of the same territory, in documentary forms, on its "Six American Families."

'But among the commerical series, "Family" is the best and most important.It takes the hour-long family drama out of the Family Hour to 10 p.m., humanizing both the 8 p.m. pap and the 10 p.m. gore.

The genre needed "Family." Some of TV's families have folded quickly - witness "Apples's Way," "Beacon Hill," "The Family Holvak." The new "Eight Is Enough," is old-fashioned and obvious. "Little House" is NBC's most popular series, but it appeals primarily to children. "The Waltons" isn't what it used to be, and Carol Evan McKeand, its story editor for two of its best seasons, is now the executive story consultant on "Family." "Family" co-star Gary Frank says "The Waltons" is about "11 people who have all had frontal lobotomies."

The "Family" family, the Lawrences of Pasadena, show no signs of such surgery. They're rather witty folk who avoid emotional extravaganzas and excess verbiage. When a hospital scene began to turn soggy, Dad protested: It got a bit maudlin there," and Mom smiled. The Lawrences are less certain about eternal verities than the Waltons, this being 1977, but somehow they survive. This being 1977, they are also wealthier and less numerous than the Waltons.

Their fortunes are rising. A large and growing fan club within the TV/film industry is expected to make "Family" a strong Emmy contender (if an internecine struggle within the TV Academy doesn't shut down the whole ceremony). In the ratings, the show has generally taken its time slot all but once this season. When CBS extracted "Kojak" from ratings trouble on Sundays and moved it up against "Family" on Tuesday, the ace cop was widely expected to shoot "Family" down. "Family" won every match.

There are a few troublemakers who wonder if "Family" is what it used to be. Why has a show built on such distinctive understatement used increasingly melodramatic plots? We've seen a terrorist seek refuge with the Lawrences. We've seen a two-part episode in which Dad loses and then regains his sight. The direction, the acting, the dialogue remain low-key, but they struggle against plot contrivances that wouldn't be noticed in a series less devoted to verisimilitude. Can this "Family" be saved?

Nothing seemed in danger during a recent day on the "Family" set at 20th Century-Fox. And no one seemed especially euphoric over the show's recent success. Tennis champ Chris Evert showed up as a fan of co-star Kristy McNichol, 14, and said "Family" is her favorite show. A cake was brought out for co-star James Broderick, marking his 50th birthday. Shooting of the season's last episode continued calmly. People talked about their vacations.

The mood fit the show - friendly, secure, not too excitable. The set itself, the Lawrence home, was designed under the supervision of Mike Nichols as "a house that looks like people live in it, not as a set designed to let cameras pass through," says Leonard Goldberg of Spelling-GoldbergP Productions. And it's true - there are coffee stains in the kitchen sink. Childhood pictures of the cast members are on the piano. Co-star Sada Thompson received a fan letter praising the accuracy of the light entering the living room window.The gave it to the lighting staff.

The Lawrences, it appears, have been living there for years. It's an optical illusion. Networks don't necessarily jump at the chance to do dramas about basically quiet people at 10 p.m., and "I'm amazed we're still on the air," says producer Nigel McKeand.

It began, says Goldberg, when he and partner Aaron Spelling were in Spelling's kitchen one day, talking about the Louds, the Santa Barbara family profiled in cinema verite style on PBS in 1973. "Forgetting about something that far out," recalls Goldberg, the pair realized "there wasn't one drama on the air about a contemporary American family." "Chopper One," a flop that was canceled after 13 weeks, was conceived at the same occasion. (A lawsuit has been filed by writer Jeri Emmett Laird claiming she submitted the "Family" idea to ABC and Spelling-Goldberg. Goldberg says he has "absolutely no recollection" of the submission.)

Jay Presson Allen wrote a "Family" pilot for Spelling-Goldberg with the working title "The Best Years." But ABC wasn't interested until Mike Nichols, who had been hired by ABC to develop ideas, suggested his friend Allen's script. Spelling-Goldberg and Nichols produced the pilot jointly. After Nichols joked that the show might be called "Acceptable for the Family Hour," says Goldberg, the title was pared to "Family."

ABC took no further action, recalls Goldberg, until Silverman's first day on the job as ABC programming boss Silverman called Goldberg that day to say he had "fallen in love" with the "Family" pilot and predict it would be "a big hit." He ordered a batch of scripts.

Nichols and Allen weren't interested in regular television work, so Spelling-Goldberg found a new production team headed by Nigel and Carol Evan McKeand. They prepared five more "Family" episodes, and ABC presented them as a mini-series last spring. Then after considerable suspense, "Family" won a slot in last fall's schedule.

The early renewal for next season is important to the makers of "Family" practically as well as symbolically. They blame most of the problems in this year's scripts on the speed with which they were forced to work after ABC gave them such a late go-ahead for the series.

"Now that ABC gave us an early pick-up, we'll be able to do more justice to the show," says Goldberg. He concedes that some of this season involved "more ordinary material than we're capable of handling" and says next season will feature "no kidnapping or life and death material. I hope we won't have to resort to melodrama instead of drama."

The McKeands agree the terrorist episode was a mistake. But Carol McKeand also observes that "you can't do an hour about Buddy losing her comb, especially to 10 p.m."

Nigel McKeand brings up "that hideous word 'soap opera'" and explains why it doesn't describe "Family," speaking from his experience as an actor for a year on a daytime soap. In a soap, he explains, "there is endless discussion. For a year I said exactly the same thing. There is enormous predictability, enormous self-pity."

In comparison, discussions on "Family" frequently leave a lot unsaid, offer a few surprises and seldom indulge in self-pity. Furthermore, adds Nigel McKeand, "we're very careful to use ordinary humor, the inherent wit which fairly articulate people use when they're in a tight spot." Soap operas do not.

But surely ABC has tried to exploit whatever suds are inherent in "Family"? Well, says Nigel McKeand, "a 'soft' show might get a 32 (rating) and a slightly nippier show will get a 40. The temptation is considerable , but the pressure has been minimal." The McKeands have not even talked with Silverman since the show began.

It's obvious, however, that the ABC ads for "Family" emphasize the nippiest aspects of each episode. Subtlety is not yet television's top priority. Most writers for TV drama do cop shows, says Carol McKeand, and "if they're in a jam, they fire a gun. It's only a hole in a body. It there's a hole in our show, it's an earthquake. If the episodes aren't tightly constructed, they're nothing."

"I really do hate the violent shows on TV," says Nigel McKeand. The McKeands have a 3-year-old daughter, Sarah, and "When you have a little child, you suddenly realize what people are shouting about." Sarah entered a room the other day where a TV set displayed a man hitting a woman on the mouth. "Immediately I thought 'Don't watch it, Sarah," says Sarah's father, grimacing slightly as he recalls his reflex. "It's really very nasty."

Don't ask Sarah McKeand about "Family." It comes on past her bedtime.It has actually shown us unmarried couples in bed together. Call it "Unacceptable for the Family Hour."