TRAVERSE CITY, MICH., JULY 28 -- The Republican presidential race, in the eyes of GOP governors, has become largely a two-man contest, with Vice President Bush well out front of Senate Minority Leader Robert J. Dole (Kan.).

Interviews with most of the 24 Republicans at the National Governors Association meeting, which ended here today, produced repeated comments that the Iran-contra hearings have not turned into a serious threat to Bush's candidacy and that his methodical personal campaigning and organization work have made him the candidate to beat.

California Gov. George Deukmejian, saying that the vice president "is further along than other candidates," told reporters "he has benefited from the Iran-contra hearings. There was speculation early he might be wounded and that has not happened, so it's given him an opportunity to get additional financial and volunteer support."

Across the country, "Bush is the heir apparent," said Rhode Island Gov. Edward D. DiPrete -- adding, as did several others, that the vice president "has to set out his own agenda" to hold his support.

Bush aides here said he will do that in an intensive speaking schedule between his formal announcement, planned for mid-October, and network-sponsored television debates in early December. For some GOP governors, that will be none too soon. "I told him three years ago he had to strike out on his own and be his own man," said Oklahoma Gov. Henry Bellmon. "He hasn't done that yet."

Despite such comments, Bush is well out front among the governors. His aides say that they have realistic hopes of expanding his list of formal endorsements from the present four governors to as many as 14 before the first primary and can see no more than three governors supporting other candidates, including their home-state allies. Several governors are planning to remain neutral, either because they also are running or because their states have early contests and their supporters are split.

Except for such early primary states as Iowa and New Hampshire, most of those interviewed reported little organized support for the other GOP contenders -- Rep. Jack Kemp, Pierre S. (Pete) du Pont IV, Alexander M. Haig Jr., Paul Laxalt and Marion G. (Pat) Robertson.

Iowa Gov. Terry E. Branstad, who intends to remain neutral in his state's Feb. 8 caucuses, said the momentum "has swung back to Bush again" after Dole had made inroads early this year.

He credited the shift to "very good organization, including some of the early Reagan people, and a good job by Bush himself in keeping in touch. He got out front early on the ethanol issue" -- a plan for converting surplus grain to fuel -- "and he hit a responsive chord with Iowans."

Branstad also noted that Dole's gains came early this year when many "wondered if Bush would be implicated" in the Iran-contra investigation, "but nothing has come out that would be damaging."

New Hampshire Gov. John H. Sununu, a Bush supporter whose state will hold its leadoff primary eight days after the Iowa caucuses, said he thought "the administration has come off well" in the Iran-contra hearings and the "hard, hard feelings toward the investigating committee have rubbed off on our senator." He was referring to Sen. Warren B. Rudman (R-N.H.), vice chairman of the Senate panel and a likely leader of Dole's effort in New Hampshire.

Bush is judged to be ahead in Alabama, California, Florida, Illinois, Indiana, Maine, New Mexico, Oklahoma, South Carolina, Texas, West Virginia and Wisconsin. In most cases, the governors of those states are expected to endorse Bush, if they make a choice.

Dole's strength is concentrated in the Midwest. Kansas Gov. Mike Hayden is supporting his senator, and governors in South Dakota, Nebraska and Missouri -- although neutral -- all report strong support for Dole in their states. The same is true in North Carolina, the home state of Dole's wife, Secretary of Transportation Elizabeth Hanford Dole, where Gov. James G. Martin, a neutral, said Dole has the best organization.

Surprisingly, the most serious doubts about Dole's candidacy were raised by Oklahoma's Bellmon, who served for 12 years with Dole before retiring from the Senate in 1980. "I like Bob Dole as a person," he said, "but he's very deficient in the international area, where Bush is very strong."

Bellmon also expressed concern whether Dole has abandoned what he called "the caustic, destructive, hip-shooting" tactics he used as the 1976 Republican vice-presidential nominee.

Some Republican governors criticized Bush, mainly for the lack of a visible effort to define his positions and goals. DiPrete said, "I think he's so loyal to Ronald Reagan he doesn't even want to suggest there are challenges this administration hasn't met. But the 1990s have different challenges, and he's got to address them."

New Jersey Gov. Thomas H. Kean said du Pont "is the only one of the candidates who's talking about the challenging issues," adding, "I've had more deep and intelligent discussions of public issues with George Bush in private than I've ever heard him make in public."

"He has to find a way to draw the line between his past and his future," Maine Gov. John R. McKernan Jr. said, "and I think he's beginning to do that." South Carolina Gov. Carroll A. Campbell Jr., also regarded as a Bush ally, said, "Bush is walking a fine line now, but I think as soon as he crosses the line and becomes a candidate, he'll be able to say a little more."

Kemp and du Pont are credited with growing organizations in the early states and in scattered small states later in the calendar, while Haig's and Laxalt's support is viewed as spotty or nonexistent by most governors. Robertson is a bit of a mystery -- with Campbell seeing strong organizational efforts in South Carolina while Martin said the television evangelist seems to have lost support in the wake of the PTL scandals that have drawn heavy publicity in the home base of Jim and Tammy Bakker.