Within weeks of his election in 1978, Nevada Gov. Robert List was embroiled in a controversy over his accepting free food and drink from a hotel-casino under state investigation.

The next four years did not go much better. He hedged his position enough on the plan to bring MX missiles to Nevada to alienate both its supporters and opponents. The national economy plummeted, chilling the state's tourist industry just as List put into effect a scheme to make state revenues heavily dependent on tourist sales tax dollars.

The 46-year-old Republican's negative rating in the polls hit record levels. The state's popular attorney general, Democrat Richard Bryan, decided to run against him.

And while List managed to win the Republican primary, the "none of these candidates" line, which is unique to Nevada ballots, got 19.5 percent of the vote.

When List and Bryan met recently for a televised debate here, the governor's stock had fallen so low that Bryan's staff seemed worried about little more than powdering their candidate's shiny, balding forehead. Two recent polls showed Bryan at least 21 percentage points ahead of List, which is why Democrats count this race in their hopes of picking up six or eight governorships this year.

Bryan, 45, is an intense campaigner who was first elected to the state Assembly in 1968 and cautions that List still could make a comeback. He warns of List's ability to woo voters with a genial personality and a well-financed campaign.

"List personally is a very nice guy," said Bryan's campaign press secretary, Joe Merica. "He's humorous, the kind of guy you would like to have a beer with."

During the television debate, List made an effective, self-deprecating appeal for understanding.

"These last four years have been extremely difficult, not just for us in Nevada but for people in the United States and in the rest of the world," he said.

After the debate, he contended that his own private polling indicated he was catching up to Bryan. "As of a couple of weeks ago," List said, "I was a bit of an underdog, but now I feel we have got momentum and we'll peak at just the right time."

Countless doomed politicians have said the same, but List is making some headway with a popular tactic in this conservative state -- labeling his opponent a foggy-headed liberal.

Bryan repeatedly has had to defend his votes as a state legislator against a death penalty law and an antipornography law. He voted against the death penalty in 1969, but changed his mind and voted for capital punishment on three occasions after that.

The antipornography law he opposed was, in his view, unconstitutional, but during the debate List pointed out that it survived court review and remains on the books.

Bryan has no monetary advantage over List; both campaigns expect to spend about $1 million.

Bryan has been able to do to List what Republican Pete Wilson is doing to Democrat Edmund G. (Jerry) Brown Jr. in neighboring California, however -- weigh him down with the failures of being a governor. But since List is not a Democrat, he cannot blame the state's economic troubles on the Republican administration in Washington.

"Are you any better off than you were four years ago?" Bryan asks campaign audiences. "For the first time in 50 years the administration in Carson City has failed to protect us from the effects of a national recession."

Bryan charges that List has failed to spend money where it would do the most good -- in tourist promotion. The state must prepare now, he says, to lure tourists going to the 1984 Olympic Games in Los Angeles.

In a state where some of the governor's most important powers concern state investigations of the gambling industry, the gaming control board has also become a source of debate.

Bryan has complained bitterly that List's appointees on the board cut the attorney general's staff off from some confidential information, on the grounds that the attorney general's staff had leaked sensitive material to private law firms. Bryan also recounts List's attempts to lobby for gambling licenses for certain interests, which List justifies as the duty of any governor to encourage more industry that will bring jobs.

List distributes copies of his wife's cookbook, shows off pictures of his three children and throws himself on the mercy of the voters.

"I know I haven't pleased you all the time and frankly I've made my share of mistakes," he said on television, then added, "But I get blamed for everything from the Mexican bank failures to the heartbreak of psoriasis."