With the appointment of William E. Brock to run his presidential campaign, Sen. Robert J. Dole (R-Kan.) has taken another stride toward clearing two of the three hurdles in his effort to firmly establish himself as the challenger to Vice President Bush.

"Dole is in an excellent position," Charles Black, manager of the competing campaign of Rep. Jack Kemp (R-N.Y.), conceded. Black added, however, that Dole faces the difficult strategic decision "whether to compete as a conservative, to firm up the moderate support he has acquired or to continue to send mixed signals. He's greatly cross-pressured."

In the 11 critical tests of strength before the onslaught of primaries on "Super Tuesday," next March 8, Dole is widely viewed a competitor with the potential to win in six or more of the states holding primaries or caucuses from Jan. 27 through March 5.

At the same time, Dole has demonstrated an ability both to raise money -- $7.9 million -- and to set up organizational beachheads in battleground states adequate to sustain the early stages of a campaign against Bush, the clear front-runner.

The selection of Brock, a former chairman of the Republican National Committee, adds legitimacy to Dole's claim that he no longer insists on functioning as his own manager as he effectively did in 1980, when his presidential bid ran behind "undecided" in the Iowa polls and received fewer than 700 votes in the New Hampshire primary.

The remaining hurdle facing Dole is formulation of a set of coherent themes -- the development of a campaign message. He has been experimenting with a semipopulist line designed to set off his rural Kansas roots from Bush's affluent New England ties.

Dole, however, has so far carefully avoided linking his candidacy with any ideological wing in a warring Republican Party, avoiding many of the tests of the GOP primary process that could prove to be time bombs exploding in the general election. His opposition, however, is sure to pressure Dole to abandon this relatively safe position, as Bush attempts to stake out a moderate posture among the candidates and Kemp seeks to mobilize the right.

Over the past 6 1/2 years as Senate Finance Committee chairman and Republican leader, Dole has wavered from liberal tax reformer to conservative foe of abortions and gun control. Most recently, he has shifted from leading advocate of the Supreme Court nomination of Robert H. Bork -- the current conservative cause celebre -- to a careful avoidance of the limelight as the nomination approaches near-certain defeat.

A number of Bush aides contend that the vice president is better off with a nonideological candidate emerging as the leading challenger because, they contend, ideologically committed candidates often have a base that will repeatedly bounce back from defeat.

"Running a campaign of electability and winnability is . . . not good at all if you don't win," one Bush supporter argued.

It is, however, in the trenches with Bush where Dole has experienced the most success, particularly in the key state of Iowa. Dole's history of support of federal assistance has produced a base of support extending beyond the party establishment into the agricultural community, including 50 of 98 chairmen of local Farm Bureaus and much of the leadership of pork, corn, soybean and other commodity groups, according to aides.

Along with Iowa, Dole is fully competitive in such other pre-"Super Tuesday" states as Hawaii, Vermont, South Dakota and Wyoming, and would seem to be sure of victory in the contest in his home state, Kansas, according to aides.

In the GOP nomination fight, strong performances in some of the early states, with at least one or two victories, is widely viewed as critical to any campaign seeking to go into the 17-state contests on March 8, including almost all the South, with both momentum and fresh cash.

Within this highly fluid universe of early contests, Dole is at rough parity with Bush in terms of the number of states either is likely to win, even though Bush had a decided lead in national public opinion polls.

While Dole is considered to hold an edge over Bush in Hawaii, Iowa, South Dakota, Kansas and possibly Wyoming, Bush is viewed as holding the advantage in New Hampshire, Maine, Vermont and South Carolina. Dole is competing with Kemp for Minnesota's delegates, a state Bush forces are privately conceding for the time being, and Marion G. (Pat) Robertson has a fragile hold on front-runner status in the Michigan caucuses.

Bush forces are trying to turn Iowa into a high-stakes contest for Dole that will make or break Dole's campaign. "If he loses Iowa, he's like an iceberg hitting the tropics," said Rich Bond, deputy Bush camapaign manager. "It is a must state for him. It is the only state where he is the front-runner to the front-runner. If he can't produce there, where can he produce?"

At a different level in the campaign, Bush appears to be more than willing to become the target of Dole's populist spears. "You don't have to be born to wealth," Dole tells audiences. Without mentioning Bush, Dole notes, "I don't come from any powerful family with any powerful friends and powerful parents, and I've made it the old-fashioned way."

Just this past week in Dearborn, Mich., Bush walked right into Dole's populist trap, telling an audience that he lost an Iowa straw poll to Dole and Robertson because "a lot of people that support me, they were off at the air show, they were off at their daughter's coming-out party, or they were off teeing up on the golf course. . . . "

Last month, a Bush aide challenged Dole's populist credentials by asking, "What's Bob Dole going to do: rent a trailer and invite all the New Hampshire police chiefs to see him in his Airstream?" Dole then held a news conference in front of an Airstream trailer at a law enforcement conference in Des Moines where he said: "My hope is the American people fully understand which of the candidates represents America. . . . Not everybody lives in Kennebunkport," the Maine resort where Bush has a summer home.