What do Alexandria, Va., Stamford, Conn., Newton, Mass., Evanston, Ill. and Berkeley, California have in common? Each is a small city that has undergone significant change over the past two decades in dealing with problems that their neighboring large cities have confronted over the same period of time. This situation in metropolitan area cities of approximately 100,000 people needs attention.

There has been more emphasis, and consequently more understanding, of the turmoil endured by large-city school systems. Whether it was a strategy of avoiding, delaying or confronting complex urban problems, the major cities' school systems experienced damaged reputations and significant changes in their school populations.

Though there are distinct differences between the cities listed here, there are important similarities. Each of these places is next to a larger city (Alexandria/Washington, Stamford/New York City, Newton/Boston, Evanston/Chicago, Berkeley/Oakland and San Francisco). Each enjoys a favorable tax base, a high median income and a well-regarded public school system. So why worry about them when others are in much deeper trouble?

Since these are urban school systems, they must compete for funds with other city agencies facing their own serious problems. For years these local funds have been raised primarily through property taxes. But the percentage of the population with children in public schools has been decreasing steadily while the percentage of people on fixed incomes has been rising, making it more difficult for school board budget requests. There are other factors affecting these smaller urban school districts:

* declining school enrollments;

* changing school populations, with the percentages of minority students rising steadily;

* desegregation plans developed and put into effect;

* bilingual and English-as-a-Second-Language programs growing steadily;

* increasing competition from private and parochial schools;

* losses off federal funds;

* losing battles with the states in attempts to change basic aid formulas that do not recognize adequately what is happening in these cities. While they may appear affluent, their public schools welcome and educate a wide variety of students, including a growing percentage of poor children who begin school with many disadvantages.

Take Alexandria: from my obviously biased position it does have a fine public school system that competes favorably with suburban schools surrounding it. But to compete well is expensive:

Between 1971 and 1982, enrollment in Alexandria dropped each year, from 16,566 to 10,543. During this period, Alexandria desegregated its schools voluntarily, redistricted school zones and went through a school consolidation program that created tremendous controversy.

October 1, 1982, figures show that Alexandria's student population is 49 percent black, 39 percent white and 12 percent "other," a rapidly growing category that includes students from 55 countries speaking 35 different languages. Most of these new students are refugees from Afghanistan, Southeast Asia and Central America. Visit T. C. Williams High School and you get a feeling of a United Nations. To educate this wide variety of students is costly, but it brings benefits too often unrecognized.

Roughly 20 percent or less of the total Alexandria area has children in our schools. With taxes increasing, public transportation problems growing and a responsibility for responding to the needs of the elderly, it is not difficult to understand the vulnerability of the school system at budget time. So far, the city has been generous. How much longer it will be supportive is a serious matter.

What has happened in other places nearby --Prince George's County, for example-- could happen in Alexandria. There are examples in those other cities I have mentioned: last year, Stamford's school system took a $4 million cut in its budget, resulting in school closings, reductions in programs and the loss of an able superintendent.

Another factor: the teaching staff is becoming more senior each year. In just three years, there has been a 100 percent increase in the number of classroom teachers who have 16 to 20 years' experience. Obviously, this involves costs.

Yet for now, the picture continues to be positive. The annual rate of enrollment decline has slowed to slightly more than 1 percent over the last two years, contrasted with an average 5 percent decline over the previous decade. There has been a 48 percent increase in the number of students coming to our schools from private institutions. We believe the public's confidence in this school system is increasing. But it is a tenuous situation, and it is increasingly difficult to remain competitive with suburban schools that often are inaccurately perceived as being better.

It begins to feel like a last stand. To my mind, city school systems such as ours are important, to the residents and the country as a whole. So what are the solutions?

More attention should be paid to the composition of school boards. People who are willing to give the time and effort required to preserve good school systems are invaluable, and go beyond narrow political shenanigans. We also need to work closely with the media in projecting the best image of our schools. Somehow a political coalition must be formed to produce a formula for basic aid that addresses all these conditions that require increased state aid. Cooperative planning between school systems and their municipal governments also is needed.

Unless care is given to preserving these small-city school systems, the widening of the gap between the haves and the have-nots will continue. To allow that toohappen could be to invite dire consequences for America's public schools and the concept of equal educational opportunity.