For 16 years, since he was first elected governor, George C. Wallace has dominated the politics of this state. In this year's Senate race, however, some surprising people think the string could run out.

"Some of the people around him," said Charles Snider, the manager of Wallace's last three presidential campaigns and now a volunteer adviser to the governor, "take the attitude that the people of Alabama owe it to him to send him to the Senate. If he takes that attitude, he'll lose.

"He's got to come up with a good, solid reason why he should go to the Senate. He needs a program. And then he's got to get around the state and be seen. He can't get elected sitting behind his desk."

In a similar vein, Bill Jones, a former Wallace press secretary, said, "I'd never count Wallace out, because he's a smart, tough opponent. But the polls I've seen show he's clearly lost some of his popularity in this state, and he doesn't have a gut issue to run on anymore. I think this is the year a bright young guy with no scars on him could beat Wallace."

As it happens, Jones, who left Wallace's staff several years ago to become an independent political consultant, has a candidate who fits that description, 33-year-old state Sen. John Baker.

And a poll taken last month for an other young and unscarred Wallace challenger, 37-year-old state Sen. Donald W. Stewart, tends to support the theory of Wallace's vulnerability.

The Stewart poll, portions of which were made available to The Washington Post, showed that between August and late November of last year, Wallace's share of the vote in a theoretical five-man Democratic primary field skidded sharply from a front-running 35 per cent to a second-place 21 per cent.

Except for its signal of potential Wallace weakness, the poll has limited significance. Included in it, in addition to declared candidates Wallace, Stewart and Baker, were incumbent Sen. John J. Sparkman (D), 78, and former Alabama Chief Justice Howell Heflin. Sparkman is expected to retire and Heflin then to enter the race, but neither man has made his decision public. The primary is in September.

The Stewart poll showed that in November, Sparkman would have been the front-runner, with 29 per cent to Wallace's 21 per cent, with Heflin at 12 per cent; Stewart, 7; Baker, 3, and the rest undecided.

Encouraging to Stewart was the fact that an early fall television spot campaign, for which he borrowed $54,000, moved him up from 1 to 7 per cent in the poll, and brought him even with Wallace among those who said they had heard something about him.

Wallace's reported slump coincided with the heavy press attention to the breakup of his seven-year-old marriage to Corneila Wallace, whom he married the year before he was crippled in an assassination attempt.

Wallace charged his wife had secretly "bugged" his bedroom telephone, and she accused him of "actual violence and cruelty" and suggested he was concealing hidden sources of wealth.

On Wednesday, the day the divorce trial was scheduled to begin, they reached an out-of-court property settlement giving her slightly more than $75,000 of his declared assets of $209,000. A decree formally ending their marriage will be issued within 66 days.

While some Wallace supporters are worried that the allegedly damaging telephone tape recordings may surface in some way during the campaign or that Cornelia Wallace may keep the issue alive, local reporters and editors know the case has closed.

Snider, among others, is doubtful that the divorce was the real source of Wallace's slump, arguing that sympathy for the governor probably offset any shock people felt at the breakup of a storybook romance.

Instead, his long-time manager cited the inevitable attrition of Wallace's long tenure as governor and the inevitable diminution of his patronage, power and influence as he enters the last year of his term.

Also, Snider noted, 1977 was the first year in a decade that Wallace has been without a full-time professional campaign organization. The fund-raising, publicity-generating headquarters that Snider ran was shut down after Jimmy Carter's victories in the 1976 primaries ended Wallace's presidential hopes.

"Remember," Snider said, "we spent all our time publicizing Wallace, keeping him in the forefront of attention, keeping him briefed on what was happening and pushing him hard to get cut and campaign, which he found hard to do after the shooting. I'm not sure if the people around him now do that."

In an interview the day his divorce suit was settled, Wallace appeared preoccupied with his personal difficulties and the problems in a special session of the legislature. "I'm not thinking about the Senate race," he said, even though he has formally filed with the Federal Election Commission as a candidate.

But Wallace expressed skepticism about any political difficulty. "I'm sure," he said, "the people of this state, who have supported me so generously, and have made me a national figure, will not give up that investment now."

Under a law passed last year, the primary has been moved from May until the day after Labor Day, with the expected runoff two weeks later. So the real campaigning is still some months distant.

Sparkman is officially undecided whether to seek another term after 31 years in the Senate. But several of his key campaign aides are running for other offices and his colleagues expect the chairman of the Foreign Relations Committee to step down.

The best-known of Wallace's potential opponents then would be Heflin, who is reportedly Sparkman's favorite as a successor. Heflin said today he expects to make his decision on running "very shortly," but he has set other deadlines previously and let them slip. A powerful speaker who won a national reputation for leading the overhaul of Alabama's court system, Heflin stepped down as chief justice last year in anticipation of the Senate race.

He is expected to draw strong financial and political support from Alabama lawyers and is generally regarded as Wallace's strongest potential challenger at the moment. But costs of the judicial reform he sponsored have created a controversy within the state and some political observers think Wallace could "cut up" Heflin more easily than he could either Stewart or Baker.

At 56, Heflin is only two years younger than Wallace, while Stewart and Baker both plan to cite the age differential in appealing to the self-interest of the state in electing a senator who can serve long enough to gain power through senority.

The two young state senators are similar in background and style - both being rather low-keyed, serious lawyer-legislators who were picked by reporters as the "outstanding freshmen" senators in their respective debut sessions. Baker had successfully challenged Wallace in court on pension and education financing issues, while Stewart has won a reputation as a skilled opponent of utility rate increases before the Public Service Commission.

Stewart's early TV push has made him appear the more formidable of Wallace's declared challengers, but the uncertainty over Sparkman's and Heflin's plans has made it difficult for either Stewart or Baker to raise more than a fraction of the half million dollars each thinks will be needed for a successful campaign.

Snider, who said he expects to be helping the Wallace campaign again later this year, said, "I think there's still time for the governor to get things going, but I think the longer he waits, the more risk there is to him."

Another Alabama politician, who requested anonymity, said, "I think if either of those young fellows could get into the runoff against Wallace, they might beat him. Alabama's not that different from the rest of the country. People are looking for something new."