The guessing game in Maine's three-way race for governor is what the state's popular, independent Gov.James B.Longley is going to do.

Longley, who surprised experts when he won four years ago, is keeping his campaingn promise to serve only one term and also is keeping his counsel about whom he favors to succeed him.

An endorsement from Longley, who would have been a heavy favorite had be chosen to run again, is the undropped shoe in the race between Democratic Attorney General Joseph Brennan, Republican House Minority Leader Linwood Palmer, and independent Rev.Herman (Buddy) Frankland.

Longley apparently enjoys the suspense. He has proclaimed himself neutral, but has left the door open for an 11-hour anointment of one of the candidates.

For Brennan, the front-runner, Longley's support would ensure victory. For Palmer, it could be enough to propol him into the State house, and although Frankland trails by a large margin in voter surveys, it is possible that Longley's word could ignite a new round of independent fever in Maine.

Longley came from far back in the polls in the last month of the 1974 campaign.

Frankland, 43, the minister of New England's largest Baptist church, was a Longley encouraged him to enter the race.

Although he has not received Longley's public blessing, independent Frankland casts himself as Longley's heir.

"Someone's got to carry on what Longley's started," he says. "The new parties still think that Longley was a fluke. If I win it will be a shock wave."

Frankland is a successful businessman and runs a private Christian school in addition to his church. He is spending as much or more on the campaign paigns strongly against state government interference in local matters.

"What made America great"? he asks rhetorically. "Free enterprise and local control," is his answer.

There are three statements no one hears without suspicion, Frankland jokes. "The check is in the mail"; 'Of course I'll marry you just as soon as I'm divorced'; and 'I'm from the state government and I'm here to help you.'"

Longley's success has made politicians and reporters wary of counting Frankland out as they did Longley, although the polls show Frankland has the support of fewer than 10 percent of the voters.

Democrat Brennan, 44, began the campaign as the best-known candidate after four years as attorney general, during which he was a leader in Maine's fighting against having to pay money or yiel land to Indian tribes who claimed their lands were illegally taken from them generations also.

He also has money or yield land to Indian tribes who claimed their lands were illegally taken from them generations also.

He also has moved to protect himself aginst his more conservative opponent's calls for tax relief by promising there would be no tax increase in his four-year term. Brennan says budget projections of anticipated revenue increases enable him to make this promise.

Brennan has generally liberal record. His support is based in Maine's Democratic cities and towns and in strong support from labor unions

Palmer, 56, ofter criticizes Brennan for supporting the proposed Dickey-Lincoln Dam that would flood thousands of acres of wilderness in northern Maine.

Most voters oppose the dam and Palmer says: "I'd like to be the governor who finally killed Dickey-Lincoln."

Brennan supports the dam as Maine's best available new energy source, and for the jobs it would create in the poor areas around it.

Palmer rejects polls that show him about 15 percentage points behind Brennan as inaccurate. Palmer claims he has private polls that show Brennan peaked several weeks ago and the election will be very close.

Frankland's candidacy hurt Palmer more than Brennan, but the Republican hopes that any conservatives he loses to Frankland will be more than compensated for if Republican Rep.William Cohen, in his Senate campaign, and Republican Rep.David Emery, who is seeking reelection, make strong showings for the Republican Party on election day.

The biggest help, however, would be a blessing from Longley.