The next mayor of Takoma Park is likely to be a City Council member, who as part of a recent political transformation helped shift the city's highly publicized focus on international issues, such as nuclear weapons, to the tasks of day-to-day life.

But Edward Sharp, now in his third council term, faces a challenge from council colleague Marc Elrich, who still wants his city to take more of a world view.

As the council prepares to vote Dec. 10 on a replacement for Mayor Stephen J. Del Giudice, who earlier this month launched a write-in campaign that won him a seat on the Prince George's County Council and a place in state history, the two council members have emerged as the leading contenders.

Their visions for the city do not differ significantly. More often than not, they vote on the same side.

But it is the relatively conservative style of Sharp, who has gained the early support of most of the council, and the more outwardly passionate spirit of Elrich that council members will weigh as they decide who should fill out the remaining year of Del Giudice's term.

Sharp entered city politics in 1985 on a slate with Del Giudice, both appealing to voters to oust controversial Mayor Sammie Abbott and pay renewed attention to the city's financial well-being. Elrich, on the council since 1987, was an Abbott supporter.

Del Giudice will resign as mayor Dec. 3, the same day he assumes his role on the Prince George's Council. The City Council is required to appoint a mayor within 60 days of the resignation, according to the Takoma Park charter.

Although the city will accept applications through Nov. 30 from residents interested in the city's top office, council members agree that the next mayor is likely to come from their ranks. In that case, the council must appoint a replacement for that position.

If a council member does make the move to the $4,800-a-year mayor's post, he would have to give up his vote.

In Takoma Park, the mayor sets the agenda, but only council members vote. That will change after the November 1991 election, when changes to the city charter take effect, giving the mayor a vote and reducing the number of council members from seven to six.

Sharp, 41, who writes grant regulations at the Department of Energy, and like Del Giudice lives on the Prince George's County side of the city, said that as mayor he would urge a review of the tax rebate system between Takoma Park and Montgomery County. He said he believes the city is not receiving its full share, and would like Takoma Park to help Montgomery County accelerate its recycling program.

Sharp, who also serves as mayor pro-tem, has received preliminary support from council members Gregory Hamilton, William Leary and Hank Prensky.

Council member Jim Douglas declined to comment and Del Giudice has said he will not make an endorsement.

"I don't do this with any pretense of getting the four votes," said Elrich, 41, who was defeated in September's crowded Democratic primary for the Montgomery County Council's District 5 seat. "I think there are issues to be raised. I don't view {Sharp} as the enemy."

Elrich, who until recently worked at the Takoma Park-Silver Spring Co-op market, cited among his civic accomplishments his work toward the passage of a bond proposal that raised money to make long-needed street repairs. He favors bringing Takoma Park wholly within Montgomery County's borders and wants the city to be more vocal on several school, development and social issues. His vote this year for a 4 percent ceiling on rent increases, compared with Sharp's vote for a 5 percent limit, illustrates that he is a stronger ally of tenants, Elrich said.