Four of the eight colleagues of Chief Judge Theodore R. Newman of the D.C. Court of Appeals have taken the unprecendented action of openly opposing his renomination as the court's top judge when his term expires next month.

The conflict between Newman and his four critics on the District's highest court broke into the open last week when the judges wrote a letter to the city's judicial nominating commission asking that he be replaced as chief judge.

The letter hinted there are both edeological and personality splits on the court and questioned Newman's leadership. The letter did not explicitly name Newman, but rather described the qualifications which the four associate judges said the chief judge should have.

"That is why we view . . . the commission's designation of a member of this court as chief judge as a decision of great significance. At no other time has this been more true," the four judges said in their letter.

The four judges who signed the letter were John W. Kern III, George R. Gallagher, Frank Q. Nebeker and Stantley S. Harris.

Two of the letter writers -- Kern and Nebeker -- ahd sought the chief judgeship four years ago. The four Newman critics often are in disagreement with position taken by Newman and the liberal wing of the court.

The judical nominating commission must select a new chief judge from among the sitting members of the court. Newman said yesterday that because the matter was pending before the commission, it would be "inappropriate" for him to comment on the judges' letter.

The four who signed the letter eliminated themselves as candidates for the chief judgeship. At the same time, they suggested that Judge William C. Pryor, the most recent appointee to serve on the appellate court, would be their first choice to fill Newsman's slot. But the Newman critics also said that Judge Catherine B. Kelly would be acceptable to them on the grounds that she is the court's most senior judge in terms of length of service.

Ironically, Newman lobbied strongly against Pryor's appointment to the court last year in favor of another, more liberal judge. Pryor, who like Newman is black, has told friends that he was upset at Newman's action although Newman eventually testified on his behalf after Pryor was nominated by President Carter.

The complex struggle between Newman and his fellow judges provides a revealing glimpse into courthouse politics in the District of Columbia.

Newman, 45, a Republican, was appointed to the bench in 196 by President Gerald R. Ford. It made Newman the black in the nation to head a state-level court system.

He took an activist's role inleading the court, and unabashedly told conferences of lawyers and judges that he would institute a "five-year plan" for the court even though he was named chief judge for only four years.

Newman has said the plan would bring more openness and efficiency to court operations. In one change, Newman had the court's internal operating procedures published and made publicly available; he also said the court would cooperate with outside groups if they wanted to monitor the court's operation.

He has written significant decisions upholding the mayor's power under the D.C. home rule charter and taken a strong stand against incompetent legal representation. AMONG HIS MOST NOTED CASES, WHILE SERVING ON THE D.C. lSuperior Court in 1974, was a ruling striking down "the corroboration requirement" in rape cases, meaning that a woman's allegations that she was raped need not be supported by another eyewitness.

But he apparently has rubbed his appellate court colleagues in some ways they did not like.

He is at times considered temperamental and blustery, yet extremely self-confident in his legal and administrative abilities.

Lawyers who have argued cases before Newman say he is prone to interrupt them while they are trying to answer questions posed by other judges. The letter sent to the nominating commission said that "disagreements about cases and procedures are certain to occur. However, the proper, courteous and thoughtful handling of those disagreements in a constructive way is essential to achieve open and free discussion and congenial resolution.

"The judge who occupies the position of chief judge sets the tone in those exchanges and decisions. As presiding judge at hearings when he sits and in other public forums, he or she must reflect a dispassionate deliberative air," the letter said.

The letter described a court "staff morale problem" and said the person selected for the chief judgeship had to "bring a consistently calm and steadying influence to bear upon the court and staff with an ability and a temperament which will enable him or her to review collegially with all its members the steps to be taken on current problems."