The Baxters live right next door, but in more than 50 major markets at once. And when "The Baxters" premieres on TV stations in those cities -- including Channel 7 in Washington tonight at 7:30 -- it will be the only outwardly innovative new series of the TV season.

It may also quickly turn into the most talked about.

A network didn't innovate this baby. Norman Lear, who gave the world The Bunkers at the top of the '70s, gives us The Baxters in the bottom half of the ninth.

Lear was so enamored of the idea that he bounded out of semi-retirement from television in order to produce, rewrite and promote the show himself.

The Baxters are an allegedly typical middleclass American family who each week spend 11 minutes grappling with a relevant social or domestic problem. Stations follow each vignette with some form of community response locally produced. It could be a live phone-in from viewers or, as with Channel 7, a pre-taped thrashout with an invited studio audience. But somehow, The Great Unseen will be heard.

"It's totally intriguing to me," says Norman the Indefatigable. "I never thought communication stopped with the taping of an episode of anything, anyway; in fact, it starts with that." Eventually Lear will take "eight to 10" of the 10-minute response sessions from different cities and splice them together as a kind of town-to-town meeting of the air, a one-hour special that stations airing "The Baxters" will be able to run if and whenever they want.

What makes the show different is that stations airing it don't just slap the tapes on the air and collect ad revenues. They are required to produce, 51 percent of each half-hour themselves; only the first 11 minutes come pre-packaged from Lear's T.A.T. Communications on Sunset Boulevard.

In essence, stations have to help make "The Baxters" that rarest form of television, two-way communication between the viewer and the viewed.

It's something of a sweetheart deal for broadcasters as well, since "Baxters" can be counted toward their community-programming commitment at the FCC. This is like having your cake, eating it too and then learning that it has fattened nothing but your wallet. It could only happen in a business like the television business, which there is no business like.

Although Lear has earned a reputation as the king of controversy in television, some viewers may still get an unexpected jolt from the intimacy and candor of "The Baxters." Among the tougher topics: sharing birth control responsibilities in a marriage, whether a wife should submit to sex-on-demand from her husband, the fitness of homosexuals as public school teachers, forced busing even that surest of angry letter-baiters, incest.

"Well, 'incest,' that's such an inflammatory word," says Lear. "We deal with a relationship on one show that we say took place a lot of years ago between a grandfather and a child, not something that is happening in the present. It's really physical abuse of a child. You know this problem of too much attention to a child by an older adult in a family is something of phenomenal proportions. Now that we're finally free to discuss it, it becomes something that can be dealt with and treated."

The episode about birth control finds Mr. and Mrs. B, embroiled in a blunt bedroom battle over the mechanics of family planning. After 20 years of marriage, Mrs. Baxter announces she has had her I.U.D. removed and declares that birth control will be Mr. Baxter's problem from now on. She suggests he visit a drugstore, obviously to buy contraceptives.

"Those things are so unromantic," he complains. "They're just plain awkward." She suggests a vasectomy. "It's a simple operation -- cut and dried," she tells him. 'he doesn't look very convinced.

An episode in which the husband, drunk and spry, all but rapes his wife, is even stronger. The argument stops being civil; he throws her down on the bed and growls. "You're my wife; now act like it." She: "Don't force me." He: "Don't make me force you!" She: "I want to feel like you want me, not just my body."

There aren't a million laughs in this one, folks.

In many of the shows, though, Lear's genius for intermingling social comment and entertainment blooms again; at its best, "The Baxters" is the kind of personal theater for a mass medium that Lear made art with "All in the Family." And in "Baxters," there's really more social questioning than social commenting. Easy answers are not beamed in just prior to fade-out.

No stations have made even a peep of complaint, either, about the explicit content of some of the programs; partly because the public-service angle acts as a protective shield. Lear in fact made the marital rape show first and used it as the pilot to sell the series.

"I thought we'd start with a very difficult subject, just to prove it could be handled in 11 minutes," he says. "I remember when we started 'All in the Family,' I said I wanted to show 360 degrees of Archie Bunker right off, on the theory that you can't get wetter than wet and at least the network and I would be getting wet together. Of course, a couple of weeks later, there they were asking me, why did I have to do a show about impotence, why did I have to do a show about menopause, and so on.

"But believe me," Lear says, "I know the audience, and they're not going to jump up in arms over this."

Certainly there is nothing in the programs to equal the sniggering or smirking of such feeble titillations as ABC'S "Three's Company" or syndicated shows like "The Newlywed Game" and "The Dating Game." And no one can say that the list of "Baxters" subjects is something Norman Lear has foisted on America, because the list was drawn up on the basis of suggestions from the participating stations themselves.

Among the other dilemmas to besiege the Baxter house over the next 24 weeks: what to do with elderly relations who can't care for themselves, should a teen-age daughter be allowed to have her boyfriend spend the night in the house, should handicapped children be "mainstreamed" into regular classrooms or kept sequestered in special education programs and what do you do when a nuclear power plant moves in down the block?

Anita Gillette and Larry Keith are able to flesh out Nancy and Fred Baxter surprisingly well in a short amount of time, especially considering the topical exposition that has to be squeezed in. "Issues" are turned into recognizably human situations. If at times it's a little too slick, a tad too glib, at least "The Baxters" is about something; it represents ideas at work. Thus, in some respects, "The Baxters" is the show of the year.

Channel 7 is having its problems coming up with the right format for audience reaction, however. On the first show -- as on most studio productions out of local TV stations -- there is a hobbling technical shoddiness, and some awkward tape edition intrudes. These rough edges can easily be smoothed out in time, and Paul Berry makes an excellent moderator.

"I love those people at Channel 7," Lear says. "They bumped off 'The $1.98 Beauty Pageant' for this show, and it was getting a 14 rating. So for them, this is chancy."

In some cities, "The Baxters" will be shown in prime time. A few stations are even pre-empting network shows for it. In Baltimore, NBC'S "Diff'rent Strokes" will be pre-empted for several weeks by "The Baxters."

What makes this ironic is that "Strokes" is produced by Lear's own company. He stepped down from creative control over a year ago, however, It is not unfair to point out to him now that the quality of programs from the Lear Shop has fallen considerably.

After all, "Hello Larry" is not what the great Norman Lear made television safe for.

"I'm not happy hearing that, obviously," he says in response. "But other people have a right to exercise their abilities the way they can. I know their intentions are good."