Charles E. Nunley isn't sure if he or his secretary actually filled out his application for the school superintendent's job in Arlington.

But he does remember getting word from his wife that he was one of three finalists when he called home to Lorain, Ohio, from Arauco, Chile, where he was participating in a six-week cultural exchange program.

The Chilean trip was just one of many the 52-year-old Nunley has taken to learn about different educational systems in such disparate locales as the Soviet Union, Puerto Rico and England.

Now Nunley is about to journey to Arlington County, whose territorial waters and customs promise to be far different from those in Lorain, a blue-collar city of nearly 80,000 about 30 miles west of Cleveland.

For one thing, he will not find the strong union atmosphere in middle-class Arlington that he has in Lorain, and Arlington, with 152,000 residents, is nearly twice the size of his current home.

But Nunley also will find many similarities. Although Lorain has about 2,000 fewer students than Arlington, which has 15,146 students, both school districts have suffered declining enrollments in the past few years, at the same time the percentage of minority students has been increasing. In Lorain, as in Arlington, minorities account for 35 percent of the enrollment. However, Arlington includes a more diverse group -- about 12 percent Oriental, about 16 percent black and about 7 percent Hispanic -- while Lorain's minority enrollment is split almost equally between two groups -- blacks and Hispanics.

Nunley, who earns $45,000 a year in Lorain and will take over the $56,000-a-year Arlington post July 1, also will find some problems, albeit ones he is familiar with: soaring costs, school closings and reorganizations that have prompted teacher layoffs and contributed to declining employe morale.

Nunley comes to Arlington with a reputation for fiscal conservatism and for getting budgets on track -- two attributes, according to Arlington school board chairman O. U. Johansen, that gave Nunley the final edge over his two closest competitors.

When asked to described the most important skills Nunley would bring to Arlington, Johansen replied: "Managerial skills and capacity for financial management."

Johansen added that he and other board members had been impressed by Nunley's ability to handle some tough issues -- issues he can expect to face in Arlington.

"School closings, secondary school reorganization, RIFs (teacher layoffs), these are serious problems he's going to have to tackle when he gets here," Johansen said.

In Lorain, Nunley's tough stance on at least two issues -- teacher layoffs and disputes with teachers over salary issues -- brought the wrath of the teachers' union, a strong force in Lorain, and resulted in two strikes.

According to Lorain school board officials, those disputes also cost Nunley his job.

"There was such a distrust of him by the teachers group that it began to stagnate the system," said Kenneth Koscho, president of the Lorain school board who was part of the majority in the 3-2 vote against rehiring Nunley, whose term expires July 31.

Added Jerry Perch, president of the teachers' union, the Lorain Education Association: "We've had a good deal of disagreement with him. Very rarely can you accomplish anything by sitting down and talking with him . . . He impresses me as being very conservative in every area and very conservative in terms of financing."

Yet Koscho, despite his vote against retaining Nunley, describes Nunley as "a most able administrator" who "a victim of politics."

Nunley doesn't seem to have been cowed by the problems he faced in Lorain, although when told that Virginia prohibits collective bargaining by teachers, he laughed and said, "That's good news for school administrators and for boards of education."

When it comes to minority issues, Nunley gets mixed reviews in Lorain.

About 18 months ago, the Lorain NAACP chapter filed a lawsuit against Nunley and the Lorain school board over a desegregation plan implemented in 1978. The plan, which Nunley describes as an attempt to reduce "racial isolation," includes closing one predominantly black elementary school and reassigning the students to four other schools without the use of cross-town busing.

"The (adopted) plan was discriminatory in itself because it put the burden on the black community for change," said Ronald Ruskan, an attorney representing the NAACP. Ruskan and the NAACP contend that an earlier plan, which called for transfer of both black and white children, while keeping the predominantly black school open, would have been fairer to all in the community.

However, Nunley, who says he has a strong commitment to "equal educational opportunities and the elimination of racial isolation," defends the plan because it does not require forced busing. "We recognize there are some racial imbalances out there, but I don't think it's serious enough to get involved in cross-town busing," he said.

But Ruskan is still critical of Nunley: "I would have to say he is an insensitive administrator. He's more of a politician than he is an educator."

Nor does Nunley get high marks from some members of Lorain's Hispanic community."

Eugene Rivera, a Lorain school member who voted against rehiring Nunley, faults him for failing to take corrective action after a report concluded there was a disproportionate number of minority students suspended from school.

"Minority problems are not getting proper attention," claims Rivera, the director of El Centro, a social services agency serving the Hispanic and black communities.

But Nunley gets strong support from Lorain school board members Tom McConihe and Leo J. Svete, both of whom wanted to retain him.

"He is sensitive to minorities," Svete said of Nunley, whose business cards are printed in English and Spanish. "He's got a strong ego, but it's well deserved because he knows from whence he speaks. He doesn't tell you things you'd like to hear. He tells you what the facts are."

"He's tough, he's smart and I think he's fair," added McConihe. "He doesn't suffer fools gladly. He's very stern in his position once he makes up his mind, but I'm not saying he's inflexible. . .

Both Svete and McConihe praised Nunley's ability to deal with difficult issues.

"He introduced a new word to the teachers' vocabulary," McConihe said, "and that word was, 'No,' If we continued the way we were going, we would have been bankrupt. He says he doesn't care about losing popularity contests and I'm sad to see him go. He was outstanding."

Nunley, who began his 28-year career as a substitute teacher and who holds a doctorate in school administration from the University of Akron, describes himself as a moderate on educational matters, but a conservative on fiscal issues -- a point that should win him some kudos from the Arlington County Board.

Until his resignation in March, former superintendent Larry Cuban had been locked in a particularly bitter dispute with the GOP-controlled County Board over educational and financial issues. This year, that dispute continued when Cuban, just before he left the school system, submitted a proposed budget that called for $3.4 million more than the $43.5 million the County Board said it was willing to contribute to the $60 million school budget. (The country's share of the school budget finally was set at $45 million last Saturday.)

Arlington school board members, who voted 4-to-0 (board member Ann C. Broder was absent) to hire Nunley, hope he will be able to avoid some of that bitterness by winning bipartisan support from both the county board and the school board.

School board member Torill B. Floyd, a Democrat, agreed that Nunley should get bipartisan support. "I don't see why he should not be accepted by all political factions," said Floyd, who often his disagreed with the County Board on financial issues.

Nunley, for his part, already has been briefed on the peculiar nature of Arlington politics and the role of the superintendent.

"I believe schools are political so it doesn't bother me at all," said Nunley. "Running a church is political. Everything we do in society today seems to be political."