Dissension in Republican ranks became increasingly evident yesterday as a number of GOP sources described the search for a new Republican National Committee chairman as a struggle between two party factions.

According to these sources, the battle for the RNC post is directly linked to the struggle for control of the soon-to-be created committee to reelect President Bush. The conflict overlaps with a dispute over whether the chairman should be a well-known spokesman or a party mechanic.

Although the names of the finalists keep changing, the two most recent top competitors for the RNC chairmanship were, as of late yesterday, Richard Bond, a trained party operative and former deputy chairman of the RNC, and outgoing New Mexico Gov. Garrey Carruthers.

Carruthers, according to some sources in the struggle for control over the RNC post, has the backing of John H. Sununu, White House chief of staff. As a former New Hampshire governor, Sununu is said to see Carruthers as a willing ally, who might support Sununu's executive assistant, Ed Rogers, for a top position at the Bush reelection committee when it is formed.

Sununu angrily denounced this scenario. "I take no position {on the RNC chairmanship} and my staff takes no position," he said. "Anything to the contrary is just unadulterated garbage."

Bond reportedly is backed by White House pollster Robert Teeter, who is considered likely to serve as overall chairman of the Bush reelection committee. Bond is said to be backed by William Kristol, chief of staff for Vice President Quayle, and media adviser Roger Ailes and many of the 1988 Bush campaign workers.

Bond, who was deputy manager in charge of day-to-day operations for the 1988 Bush-Quayle Committee, would represent a challenge to Rogers, and the two are considered likely adversaries in the future debate over how to structure and staff the reelection committee, according to a number of sources.

"Rogers is Sununu's key to getting and keeping leverage over the reelect committee," one source said. "That is absolutely and unequivocally incorrect," Sununu said.

The debate over the next RNC chairman has little or no ideological content, according to some of those engaged in the occasionally hostile backroom discussions. Bond has been close to Bush, and played a major role in the 1980 Bush campaign against Ronald Reagan.

Carruthers supported President Gerald R. Ford over Reagan in 1976.

The selection is especially sensitive for the GOP because of the embarrassment caused by William J. Bennett's abrubt withdrawal from the chairmanship last week.