Protests by Northern Virginia teachers seeking higher pay generated new teacher complaints in Fairfax County this week, a demonstration outside Alexandria Board of Education headquarters and spread to Loudoun County, where almost half the teaching staff attended a budget hearing.

The protests, which teachers have undertaken in all of Washington's close-in Virginia suburbs, now include "work-to-the-rule" job actions in Arlington and Fairfax counties and censure of the school superintendents in those counties plus Alexandria by teacher orgainzations there.

The latest developments:

The 6,500-member Fairfax Education Association complained to school officials that administrators violated teachers' freedom of speech by barring them from discussing their job action during school activities. The administration responded that specific complaints will be dealt with on a case-by-case basis.

Also in Fairfax County, about half the 2,200 students at Herndon High School staged a 20-minute walkout yesterday morning that they said demonstrated their support for the teachers. Many shouted, "teachers, teachers, teachers" as they gathered on a grassy area in front of the school. When threatened with disciplinary action, they returned to classes.

At least 50 members of the Education Association of Alexandria marched in front of the school board's administrative headquarters on S. Washington Street yesterday in support of their demands for pay increases and greater participation in making classroom policy.

More than 380 Loudoun County teachers-just under half the entire county teaching staff-jammed the county boardroom in Leesburg Thursday night to press their pay demands. The president of the Loudoun Eucators Association told the county supervisors that low salaries have turned the school system into a "training ground for other counties."

The complaint by the Fairfax teacher organization was aimed at a directive by O. Stuart Chaplain, principal of Hunters Woods Elementary School in Reston, that teachers should not respond to a PTA questionnaire about the extent of their refusal to do unpaid work as part of the job action.

Fairfax Education Association attorney George A. Cohen claimed that the principal's action violated teachers' right to free speech.

But Chaplain said yesterday he had informed the teachers Thursday, before receiving Cohen's letter, that "they could do whatever they wanted to do" with the questionnaires. "i originally told them I needed time to look over the questionnaire."

The school administration has ordered that "no class time or school activity is to be used as a forum to promote or to discuss the recent action" of the teacher organization. Cohen said in his letter that some principals have used that directive to deprive "teachers of the right of free speech and association accorded to all citizens under the First Amendment."

In a letter to Cohen yesterday, Associate School Superintendent Jacqueline Benson said Cohen's letter is "the only indication" school officials have received that principals are misinterpreting the superintendent's directive.

"any time a problem is brought to our attention, we will respond," said school attorney Tom Cawley.

In Alexandria yesterday, School Superintendent John C. Bristol was meeting with teachers and representatives of the Education Association of Alexandria (EAA) at school board headquarters as the protesters marched outside chanting, "we care, We care."

Last week the EAA, which represents 735 of the city's 840 teachers, called for Bristol's resignation, claiming he had failed to "communicate" with them and was opposing demands for an across-the-board 7 percent pay raise and other benefits.

When the teacher protests spread to Loudoun County at Thursday night's budget hearing, the county supervisors heard statements like these:

"a bag boy in a grocery store earns more than a teacher with four years' experience in Loudoun County," said James Stone, a vocational education teacher at Broad Run High.

"the top salary for a Loudoun County teacher with 17 years experience would not qualify him for a mortgage in Loudoun County if he depended on his salary alone," said Dr. Charles Freedlander, chairman of the guidance department at Broad Run High.

"last year 20 percent of our teachers left and we expect double that amount next year," said Joyce Jackson, president of the Loudoun Educators Association."we are waiting for you to make a decision that we are worth more than we receive."

The starting salary for a Loudoun teacher is $9,500 a year. With experience and advanced education, this rises to a top of $16,500. The proposed county budget calls for a 7 percent pay increase for teachers, which would combine annual step raises and cost-of-living increments. Some teachers told the supervisors this would amount to only 2.7 cost-of-living raise for more experienced teachers. CAPTION: Picture, Half the students at Herndon High School in Fairfax County demonstrated briefly yesterday in support of teachers' demands for higher pay and benefits. By John McDonnell-The Washington Post