On Veterans Day, City Hall was locked, and a visitor, puzzling on the best way to gain admission for an appointment with the mayor, was approached by a policeman. "Oh," said the cop, when the situation was explained, "so you've come to see our new tourist attraction."

Henry Cisneros has been a kind of tourist attraction since April 1981, when he became the first Mexican American elected mayor of a major American city. Newspaper, magazine and television interviewers have been beating a path to his door to hear him expound his high-tech philosophy of economic development.

Houston is too sophisticated a city to regard its mayor as a tourist attraction. But Kathy Whitmire is one, nonetheless. And a visitor quickly finds that in the high-rise corporate headquarters that dwarf its City Hall, the men of affluence and influence are anxious to brag about their first woman mayor, in office just a year.

Texas is one of the most urbanized states, but it has never been a leader in urban government. Its cities have been controlled by small, self-perpetuating groups of businessmen and developers, handpicking the local mayors and promoting their priorities through the local press. Few people of great talent, independence or ambition have found their way to Texas' city halls.

But that pattern is changing. The election of Whitmire, 36, and Cisneros, 35, just a few months apart in 1981, brings a change of generations and of leadership styles to these cities.

Although both were born in the cities they now run, were educated in their city public schools, and are imbued with that native pride and belief in future progress that is characteristically Texas, their elections reflect real power shifts.

The infusion of new residents and new business is breaking down the old elites. Cisneros and Whitmire were opposed by most of the establishment types in San Antonio and Houston, but were able to pick up important allies among younger and newer businessmen and developers. But neither could have been elected without massive support from the minority community--the blacks of Houston and the Mexican Americans of San Antonio.

What comes through most strongly in their conversations is that both these young people want to be thought of as professionals in city government.

Cisneros, who studied with the Harvard-Massachusetts Institute of Technology urbanologists and worked on the staff of the League of Cities in Washington, moved up to the mayor's job from the San Antonio City Council. Whitmire, a widowed accountant, was city controller before she ran for mayor.

Both of them emphasize a managerial approach to their jobs and talk a jargon that might make you think their ultimate goal is to be vice president of planning for some giant corporation.

Both are Democrats, but the game they talk has almost nothing to do with traditional Democratic programs. Even less does it echo the usual laments of big-city Democratic mayors about the dire effects of federal fund cutbacks.

Cisneros' game is trying to attract high- tech industry to San Antonio. He is promoting the Austin-San Antonio corridor as a new "Silicon Valley," and is going all-out to bring in those innovative producers.

In Houston, Whitmire is trying to cope with the neglected costs of past growth, starting with a transport system that has made the freeways a day-long nightmare. Within the next few weeks, the city council is scheduled to decide the route and design of the city's first rail and/or subway system.

It would be nice to say, without qualification, that these two attractive young people are going to bring a new day to their cities. So far, both get high marks in their communities and both are strong favorites for reelection next year.

But the recession has hobbled Cisneros' drive for new industry, and the crisis in the Mexican economy has undercut one of San Antonio's main economic props -- trade across the border.

The economic slowdown has even affected Houston these last few months, stirring the first real fears of overbuilding in the office towers and causing Whitmire to recheck her revenue figures even more frequently than is her custom.

But the biggest long-term problem, which these cities share with many others, is the suspect condition of their underfinanced public school systems. Neither mayor runs the schools, finances them or is directly responsible for them. But both know that if their visions are to be realized, those schools are going to have to be dramatically improved. They are going to have to give thousands of kids who are now graduating without skills or education what they gave young Kathy Whitmire and young Henry Cisneros in the 1960s: the courage to dream and the tools to make those dreams come true.