In recent years liberalism, once so dominant in the realms of economics and politics, has clearly been losing its appeal with American voters. On the other hand, liberal ideas and attitudes have at the same time retained their old stranglehold over the major cultural institutions of our society -- the universities, the arts, the media. At this very moment, however, an extraordinary event is occurring that may portend a weakening of the liberal hegemony over American culture as well.

It all began 10 weeks ago when, to the astonishment of everyone who follows these things, a book called ''The Closing of the American Mind,'' written by a little-known professor at the Unversity of Chicago named Allan Bloom, made an appearance on the national best-seller lists.

The reason this seemed so astonishing was that ''The Closing of the American Mind'' is not only a difficult book to read but is highly conservative in its point of view. Either one of these factors, let alone both together, would ordinarily limit the sales of a work of nonfiction to a few thousand copies at most. That, indeed, was all Simon & Schuster, its publisher, expected ''The Closing of the American Mind'' to sell. Yet there it suddenly and inexplicably was on all the major best-seller lists.

At first, people in the book trade thought they were dealing with a fluke. After a week or two, they assured one another, this most unlikely candidate for best-sellerdom would disappear from the lists and into the obscurity to which, in their professional opinion, it was naturally destined.

But instead of dropping off, the sales of ''The Closing of the American Mind'' increased and kept getting bigger. From the bottom of the list it jumped to the middle, and then (overtaking books by or about such show-business celebrities as Bill Cosby, Bruce Springsteen and Bette Davis) it spurted to the very top. There for the past five weeks it has remained, the No. 1 nonfiction best-seller in the country.

What we have here, then, is no fluke. Nor is it a result of promotional hype. Though the reviews Bloom received were on the whole respectful (which was itself a surprise, given his conservative perspective), they were not what is known in the trade as ''selling'' reviews. Furthermore, Bloom's publisher did no advertising to speak of until after ''The Closing of the American Mind'' had already become a best-seller.

In short, this is a book that has found a huge audience on its own, through enthusiastic word of mouth.

Because Bloom writes in a dense and subtle prose style full of erudite references to Plato, Rousseau, Nietzsche, Heidegger and the like, we can assume that the audience he has found is drawn from the most highly educated segment of the reading public. And from everything we know about those readers, we can also assume that most of them are liberal in their thinking and generally critical of traditional values.

The question is why these highly educated liberals are flocking by the tens of thousands to buy what may be the most devastating assault on the liberal culture that anyone has produced in our time.

For make no mistake. Though Bloom's focus is on the universities, it is the broader liberal culture that is his main target.

Thus in the course of explaining how and why the universities have gone to seed, he dwells at great length on the damage contemporary liberalism has done, especially in teaching the young that there is no firm rational basis for distinguishing between right and wrong or good and bad.

In addition to demonstrating in vivid concrete detail that this liberal relativism makes for a boring and empty life devoid of meaning, drama, or romance, Bloom shows how the open-mindedness on which liberalism prides itself has turned into its opposite -- the narrow and intolerant dogmatism alluded to in the title of the book.

As if all that were not enough, Bloom goes on to charge liberalism with vulgarizing the noble ideals of freedom and equality, and he offers brilliantly acerbic descriptions of the sexual revolution and the feminist movement, which he sees as products of this process of vulgarization.

There can be no doubt that 10 or even five years ago, a book as offensive as this one is to all the liberal pieties would have been dismissed as a right-wing diatribe and would probably have vanished with scarcely a trace. Yet today it is respectfully reviewed and then rises to the top of the best-seller lists.

Whatever else this may mean, surely it tells us that even many liberals are now becoming as unhappy as most conservatives have long since been with the moral and intellectual relativism that Bloom attacks and that lies at the very center of liberal culture.

This is not to say that liberals are ready to agree with conservatives in blaming the liberal culture for the spread of violent crime, pornography, drugs, teen-age pregnancy and AIDS. Far from it. In public, liberals still blame all these pathologies on Ronald Reagan's budget cuts.

But deep down, in the privacy of their own hearts and minds, more and more liberals are apparently coming to understand that their inability or unwillingness to declare that some things are right and some things are wrong has exacted a terrible toll -- in their own lives, in the lives of their children and in the life of society as a whole.

It is still too early to tell how far, or in what direction, this new understanding will be carried. But the success of Allan Bloom's book suggests at the very least that the confidence is now seeping out of the campaign against traditional moral values that has been waged so energetically and for so long by the forces of liberal relativism within our major cultural institutions.