School Board Vice Chairman Maureen Caddigan (Dumfries) appears set to sail back into her School Board seat Tuesday when the Prince William Board of County Supervisors plans to vote on two appointments to the board. But her colleague George P. Mullen (Brentsville) may not be able to hang on to the seat he has held for 12 years.

The supervisors held a public hearing this week on nominees for the two seats. Each supervisor nominates a resident from his or her district, and the entire county board votes on the appointment.

Supervisor Edwin C. King (D-Dumfries) has said he intends to support Caddigan, a promise he made last fall during his campaign for reelection. "The only name that has been mentioned to me is that of Maureen. And usually it's expressed, 'I hope you're going to reappoint Maureen,' " he said last week.

Supervisor William J. Becker (R-Brentsville) said recently that he had not decided whom he will nominate. Mullen said he has asked to be reappointed by the March 13 deadline and will see what happens before he decides whether to seek reappointment for a four-year term in June.

County observers say that even if he is appointed Tuesday, there is still a question as to whether he can prevail in June.

As holders of the last two School Board seats with staggered terms, Mullen and Caddigan face reappointment this month. The Brentsville and Dumfries seats will be up for grabs again on June 30, when all seven seats on the board will be filled for concurrent four-year terms.

Each incumbent has been a subject of intense lobbying. Last week Mullen and Caddigan received the unanimous endorsement of an assembly of representatives of the Prince William Education Association, which governs the 1,560-teacher organization. The association has never involved itself publicly in School Board appointments, according to Cameron Yow, executive director. Also, residents of Caddigan's and Mullen's districts have been collecting petition signatures on their behalf.

But Mullen and Caddigan have upset residents from the Occoquan and Coles districts because of their votes on a school boundary change that will send those children to Gar-Field High School instead of Woodbridge. Mullen and Caddigan sided with the majority in the 4-to-3 vote Feb. 17. Since then, there has been behind-the-scenes lobbying by those who would like to see the two removed from the board.

It is customary for supervisors to consider anyone in the district who is interested in serving on the School Board, and the fact that Mullen's reappointment is in some difficulty is attributable in part to the emergence of two other Brentsville residents, Kathy Perrin and Lucy Beauchamp, each of whom has asked to be appointed to his seat.

Perrin and Beauchamp are active in school affairs countywide. Also, Perrin, a member of the school bond steering committee, has been closely involved in teen-age suicide prevention as a member of the county's Youth Services Board and the Youth Suicide Prevention Coalition.

"Because of my experience, I can look at the needs of all the children systemwide," she said.

Beauchamp, also a member of the school bond steering committee, said she has focused most of her school activities on volunteer work, particularly teaching computer use in elementary schools.

"The budget has been one of my major concerns," said Beauchamp, a statistician by training. "I think I can see and understand the budget. I'm a numbers person."

Mullen said his greatest accomplishment in his 12 years on the School Board "has been in assisting in providing proper education for the children and seeing that children and employees were treated fairly."

Mullen is a member of the School Board Finance Committee and said he considers budgetary matters to be his strong suit.

Caddigan has emerged as one of the School Board's most powerful members and is extremely popular in her district, where residents last week circulated petitions in her favor.