In the week since Prince George's County School Superintendent John A. Murphy submitted his resignation, two camps have emerged in the debate over how to choose his successor.

On one side are those who say that the school district, facing deepening financial problems, is in no condition to begin an expensive and potentially divisive national search for a superintendent. The district would be best served, they say, by an interim chief who could provide equilibrium for a year or so.

Proponents of the other school of thought insist that Prince George's cannot afford a vacuum in leadership. Rather than delaying the inevitable, they say, the school board should start an all-out expedition for qualified candidates with an eye toward having a new superintendent in place by Murphy's June 30 departure.

In the middle is Beverly Beander, president of the County Council of PTAs, whose organization is expected to play a crucial role in fashioning a consensus about the search process.

"I'm of two minds," she said. "If we go with an interim superintendent, does that mean we will just have another major change to deal with down the line? I'm also concerned that if we try to find the individual who will be permanent . . . we not rush into anything."

At stake is the leadership of the nation's 15th-largest school system.

In his seven-year tenure, Murphy introduced a popular magnet school program and raised student test scores, helping erase the district's down-at-the-heels image and establishing a national reputation for educating minority students.

But with the system facing intractable money problems, a stalled desegregation effort and rising expectations among parents, the next superintendent will need political acumen, budgetary wizardry and the ability to build consensus in a diverse community.

Tonight, at Friendly High School in Fort Washington, the county Board of Education is scheduled to hold the first of two hearings on how it should select its next superintendent. The second hearing will be Wednesday at High Point High School in Beltsville. Both meetings begin at 7 p.m.

The school board plans to decide by next week whether to embark on a national search or to fill Murphy's job from inside.

Several observers said an inside appointment would spare the school board from having to compete with nearly 20 other large school systems nationwide for the services of popular educators at a time when it faces a possible $28 million budget deficit.

"Anybody who comes in here will be facing a tremendous uphill battle, a community that will be hostile because of the budget picture," said Orphans Court Judge Angelo I. Castelli, a former school board member.

"I can't imagine too many top-notch people are going to be eager to take that on," he said.

In interviews, many people said the obvious choice for an acting superintendent would be Deputy Superintendent Edward M. Felegy.

Felegy, a 31-year employee of the school system, was the runnerup to Murphy for the superintendent's post in 1984, losing by just one vote. Since then, he has been responsible for the district's day-to-day operations.

"We need a cooling-off period," said Mignon Davis, president of the Flintstone Elementary School PTA.

"Ed Felegy would be there to provide the continuity we need to pull the county together until we find a leader the majority of the county can be happy with," Davis said.

Other administrators whose names have surfaced as possible contenders include Jerome Clark, associate superintendent in charge of personnel; Louise F. Waynant, associate superintendent in charge of instruction; John O'Connell, an area teacher specialist; Sterling Marshall, principal of Suitland High School; and Assistant Area Superintendents Joseph Hairston and Jesse Freeman.

At the same time, there is significant support for an immediate nationwide search.

"We can't afford any lag in terms of achieving equity," said the Rev. Perry A. Smith, chairman of the school district's Interfaith Advisory Council. "We need a person at the helm of this education system who will exercise influence and leadership in moving this system ahead."

"We know he is leaving so I don't see the point of delaying," agreed Joan Lockhart, PTA president at Hyattsville Elementary School. "I should hope there would be adequate candidates they could evaluate within a six-month time."

Educational search consultants interviewed last week say it is too early to identify possible candidates from outside Prince George's because the board has not determined what qualifications it is seeking. But they agreed the job is likely to attract a wide range of candidates, partly because Murphy was successful in raising the county's profile.

"Murphy has made it attractive by making it a system people look at from a national perspective," said District consultant Scott Widmeyer.

Another factor that could affect the number of applications is how strenuously parents and political leaders lobby for a superintendent who is black, several consultants said.

Ruth Brown, of the county branch of the NAACP, said recently that "the new superintendent must be black" because the student population in Prince George's is two-thirds black.

Fairfax County Superintendent Robert R. Spillane said that although such demands are not unusual, they might discourage non-black candidates from seeking Murphy's job "because they will wonder whether P.G. is really an open, equal opportunity employer. What we have heard does not seem to suggest that."

On Friday, County Executive Parris N. Glendening, seeking to erase that perception, sent a letter to school board Chairman Catherine M. Burch outlining his criteria for a new superintendent.

"This decision cannot be based solely on the issue of race, or for that matter, any other single issue," Glendening wrote.

In recent days, several black parents who are active in the schools have said they have no preconceived notions about the race of Prince George's next superintendent as long as the school board seeks out qualified candidates who believe strongly in minority achievement.

"As far as the superintendent being black, that would be great," said Barbara Dunn, PTA president at Largo High School. "But if we don't find a black superintendent, the superintendent who comes here has to be concerned with the multicultural diversity in our community and all our kids."

Educational consultant Floretta Scott McKenzie, a former District school superintendent, believes that a school system's preference for black educators should not be a deterrent for "good, strong candidates."

"A candidate who feels really good about him or herself will make that decision to seek a job solely on the basis of their qualifications and what they have to offer," she said.