HIGH ON THE AGENDA of the next mayor, as it should be on that of every taxpaying voter -- is financial management: how sound are the city administration's controls on budgeting and how are the candidates addressing the financial future of the city? There is no question that there has been substantial improvement in the city government's money management in the four years since Marion Barry took office. At that time, owing to colonial circumstances beyond the control of his predecessor, the city's books were not even auditable. But thanks to a job begun during the Walter Washington administration and completed since, the city's financial reports and practices not only have undergone auditing, but also have won high marks from the General Accounting Office.

Perhaps indicative of this strength is the failure of Mr. Barry's opponents so far to make financial management a big issue, even though they have raised some good questions about the confusion of numbers, revenue projections and cash shortfalls that have complicated anyone's armchair analysis of municipal money matters. When is a "surplus" not one, is the city spending more than it is taking in -- and how should the books be adjusted to reflect federal cutbacks and decreases in various tax yields?

The Barry administration has succeeded in keeping budget growth from exceeding inflation. In addition, when you back away from the monthly ups and downs of revenues that have fueled challengers' predictions of red ink, the city has developed a program for paying off the long-term deficit that was accumulated over the years long before the home rule charter.

Patricia Roberts Harris has argued that the real issue is not whether the mayor's revenue estimates are correct -- but whether the city "will have total disclosure and explanation of the city's financial condition and . . . planning." Disclosure has not been a serious problem, but explanations were -- for a long while. Today, there are daily reports on the city's cash flow; idle funds are invested on a daily basis, tax collections (and, yes, even those water and sewer billings) have been stepped up. New systems have been coordinated with the federal government to track down people who are not paying District income taxes; and relationships with the White House and Congress have produced reasonably generous payments to the city -- without the pre-home rule excuse-making that the city's "hands are tied" by Congress.

Mrs. Harris has proposed that a "contingency reserve" of $25 million be budgeted to cover approximately one city payroll, through a small planned savings each month. Here again, there have been small savings made in various departmental budgets each month, even if they have not been publicized and explained adequately. That, in fact, is how the administration says it will chip away at the debt it inherited. Any contingency "fund" so labeled has been considered unacceptable by Congress. Perhaps the next mayor can change that.

What about future revenues? The administration has recognized that over-optimistic reliance on sales and property taxes to generate large increases in revenue would be unwise. In planning future spending, Carolyn L. Smith, director of the city's department of finance and revenue, has noted that her agency expects no increase in the average assessment of single-family homes in Washington next year -- a result of this city's stagnant housing market. This is a revision from a modest 4 percent rise forecast earlier. Similar declines in sales-tax yields have been acknowledged in the budgeting process, and -- in the absence of new sources of money -- will have to be offset by spending reductions.

Therein lies the central financial challenge for a mayor of this city in the next four years -- and for mayors all across the country. As the National League of Cities reported last month, "The general fiscal condition of cities is poor. Expenditures are growing faster than revenues in a majority of cities sampled. . . . The outlook for cities is not going to improve until the economy does." The District -- so far -- has avoided drastic measures to maintain its balance.

Some of this relatively good fortune is due to the federal presence, and there is widespread awareness that as it diminishes, so, too, does a cushion against the kinds of severe economic jolts suffered in other areas that are dependent on certain industries. That, no matter who is mayor, will require more than sound money management. What the money is spent or not spent for will be -- and should be during this campaign -- the subject of much debate.