One of the most concrete demands students are making in the wave of demonstrations in China the past three weeks is for press freedom. One of the ironies is that this communist nation has been inching, two steps forward and one step back, toward press freedom for the past decade.

You might object to my using the word freedom in the same sentence with communist. Yes, China is still essentially a police state, and the press is still muzzled in important ways, especially on issues that pique the central government and communist party, such as student unrest.Even the English-language North American edition of Beijing Review, read mostly by foreigners, ran a ludicrous story about the first student demonstration. It said only, in its obituary of Hu Yaobang, that "several thousand cadres (officials), students and teachers went to Tinanmen Square (the great central square of Beijing) to pay last tribute to the veteran party leader."

-NONETHELESS, THE REGIME has responded mildly to its student critics. None of that business of sending tanks in to squelch protests, as was the case in Czechoslovakia when the notion that press freedom and communism were not incompatible was raised in the "Prague Spring" of 1968.

And some in the government, including the communist boss himself, Zhao Ziyang, have done more than pay lip service to the concept that the press should be a check on both the party and government, not just a party mouthpiece. The government has been relatively open the past two years, allowing much coverage of the party congress and national people's congresses. Recently, it even allowed leaders to be interviewed by the militant students on live TV. That is not the full "transparency" of government that the students want, but the direction is right.

The New York Times rewrote history in an editorial in saying that the direction of Chinese civil rights in the two years since Hu Yaobang was ousted as party chief, following the student riots of 1986-87, has been downward. That is simply not true. As one indicator, when I was teaching journalism in Beijing in 1987-88, I was often asked to lecture on American press freedom and explain our adversary system. Neither I nor my students felt at all restrained in discussing freedom or other social issues.

-THE LIBERALIZATION movement itself, as much as anything, has emboldened the students to demand more and faster reforms.

The arts are becoming far more open and daring.

Advertising has come on with a rush in all media and in billboards. It is only a smidgen in comparison with ads in the West, about what Procter and Gamble spends on network TV. But 10 years ago there was none.

Public relations also is becoming modish as the Chinese move toward private enterprise and a market economy. Press conferences with government and even military leaders have become commonplace. And when party bigwigs get heavy-handed in keeping personally embarrassing stuff out of the papers, they are sometimes exposed in the press itself.

Some Chinese intellectuals are even arguing that a new press law that has been pushed for the past couple of years should provide for some private ownership of the press, not just by government and party and their agencies.

Contrast that with the past. Until 1979, when the reform movement started, and particularly during the reign of terror known as the Cultural Revolution from 1966-76, media had no room for movement and didn't even pretend to be objective. The Central Committees decided what the people should be told. The People's Daily often made up stories to support the line. Obviously, people had no faith in the press.

Now stories are more credible. There are reports of disasters, even of hijackings. There is much criticism within the system, especially criticism of corruption, and human interest news.

-A GREAT DANGER and another of the ironies in the student demonstrations is that they may be counterproductive, resulting in repression rather than more liberalization by bringing a more conservative element to power.

A crackdown followed the student demonstrations of 1986-87, an "anti-bouregoise liberalization campaign." Many newspapers were closed and dissidents jailed, and the outlook for reforms was clouded for several months.

Just before leaving Beijing last year, I had a talk with Chen Li, editor of the the government's influential English-language China Daily.

The University of Beijing had just had some demonstrations. They stemmed from the killing of a student by toughs but turned into a call for democracy. The paper's reports of these protests were at best bland. I asked Chen why his paper, which likes to think of itself as accurate, brave, timely and comprehensive, failed to mention that the student posters and speeches criticized government leaders by name.

Chen was eager to talk, and our meeting stretched to three hours. He said the paper decides what to print in the light of China's need for consensus if it is to reach its development goals. He worried a great deal about a return to the anarchism of the Cultural Revolution, "The students have a good reason to demand more democracy at all levels, but if they take to the streets every time they have a grievance, society will have less and less sympathy for them," he said.

Not surprisingly, China Daily stories on the current demonstrations have stressed what it called the need for the people to take a firm stand against public disturbances. It insisted that the demands for democracy and elimination of corruption were goals of the government as well as of the students.

The free world feels a kinship with the Chinese students and with their goals of open expression and a government accountable to the people. We hope the demonstrations will lead to more reforms, but in their zeal, the students may actually imperil them.