His passion for buying art was amply illustrated in the National Gallery's 1979 exhibition "Old Master Paintings from the Collection of Baron Thyssen-Bornemisza"--57 masterpieces usually housed in the baron's villa-museum on the shores of Lake Lugano, Switzerland. That show clearly established that Thyssen owns the world's finest private collection of old masters.

But what's an art-collecting, billionaire baron to do when the supply of old masters dries up?

The answer--or at least part of it--is in "20th Century Masters: The Thyssen-Bornemisza Collection," which goes on view tomorrow at the National Gallery East Building.

Of course there have been bits of evidence to suggest how the 60-year-old German iron-and-steel heir has been spending his excess cash, much of it tax free since his official residence is in Monaco. Major 20th-century paintings from his collection have been turning up all over the world in loan shows such as "Edward Hopper," "Richard Estes," "Kitaj," "The Russian Avant-Garde" and "De Stijl," which is now at the Hirshhorn. Last year he bought a Winslow Homer for a record price of close to $2 million (he owns about 200 19th-century American paintings, none of them in this show). This year he added a Mondrian for more than $1 million. He's installing a computer at his 17th-century Lugano villa to help keep track of it all.

But if the baron, the baron's curator and the baron's computer know the scope of his 20th-century holdings, the rest of the art world has been panting to see what one of the art market's biggest spenders has been stashing away in various offices and residences all over the world. This show offers the first substantial snoop at Thyssen's new hoard. The results are not altogether satisfying.

Spread out over six small galleries, the show includes 66 paintings selected by William Lieberman, chairman of 20th Century Art at the Metropolitan Museum, from the 500 modern works the baron has acquired since the mid-'60s. Attempting to span the 20th century from Picasso to Popova to Pop, the exhibition begins with two knockout rooms filled with German Expressionists and dazzling Russian Avant-Gardists, but ends with a fizzle downstairs, with mediocre surrealists and second-rate, or worse, examples by big-name Americans. The most appallingly bad painting, by Mark Rothko, was made when the artist was ill, and it looks it. Several Rothkos from the Mellon collection, on view near the entrance to this exhibition, will serve to refresh the eye.

But there is much that is splendid between the extremes at the beginning and end of this show. In the first room there are two 1907 Picassos, a curious, atypical work purchased from the Nelson Rockefeller collection, and another early cubist nude that was once kidnaped from artist-critic Roland Penrose, the signature cut out and mailed to him by the picture-nappers. The work was retrieved and re-signed by Picasso. The repair can still be seen.

Past a large and important Franz Marc and a strong Expressionist work by Karl Schmidt-Rottluff, one arrives at the glory of Thyssen's modern collection--a group of early abstract paintings from the second decade of this century by Kupka, Kandinsky, Moholy-Nagy and the recently rediscovered Russian avant-garde painters Gustav Klucis, Ilia Chashnik and El Lissitzky. The latter painting is the one that National Gallery director J. Carter Brown said he would most like to own.

The subject of "The City and Still Life"--a title that appears in the catalogue but nowhere in the gallery--is the wobbly rationale for the next room. It is filled with vibrant, museum-quality paintings by Leger, Braque, Gris, Weber, Kupka (a wonderful still-life of a machine going full-tilt), and two Feiningers that may well be among the finest paintings he ever made.

From there one moves down (literally and qualitatively) to the floor below where tacky The Baron's Bounty Mixed Bag of Modern Masters at the Gallery By Jo Ann Lewis

His passion for buying art was amply illustrated in the National Gallery's 1979 exhibition "Old Master Paintings from the Collection of Baron Thyssen-Bornemisza"--57 masterpieces usually housed in the baron's villa-museum on the shores of Lake Lugano, Switzerland. That show clearly established that Thyssen owns the world's finest private collection of old masters.

But what's an art-collecting, billionaire baron to do when the supply of old masters dries up?

The answer--or at least part of it--is in "20th Century Masters: The Thyssen-Bornemisza Collection," which goes on view tomorrow at the National Gallery East Building.

Of course there have been bits of evidence to suggest how the 60-year-old German iron-and-steel heir has been spending his excess cash, much of it tax free since his official residence is in Monaco. Major 20th-century paintings from his collection have been turning up all over the world in loan shows such as "Edward Hopper," "Richard Estes," "Kitaj," "The Russian Avant-Garde" and "De Stijl," which is now at the Hirshhorn. Last year he bought a Winslow Homer for a record price of close to $2 million (he owns about 200 19th-century American paintings, none of them in this show). This year he added a Mondrian for more than $1 million. He's installing a computer at his 17th-century Lugano villa to help keep track of it all.

But if the baron, the baron's curator and the baron's computer know the scope of his 20th-century holdings, the rest of the art world has been panting to see what one of the art market's biggest spenders has been stashing away in various offices and residences all over the world. This show offers the first substantial snoop at Thyssen's new hoard. The results are not altogether satisfying.

Spread out over six small galleries, the show includes 66 paintings selected by William Lieberman, chairman of 20th Century Art at the Metropolitan Museum, from the 500 modern works the baron has acquired since the mid-'60s. Attempting to span the 20th century from Picasso to Popova to Pop, the exhibition begins with two knockout rooms filled with German Expressionists and dazzling Russian Avant-Gardists, but ends with a fizzle downstairs, with mediocre surrealists and second-rate, or worse, examples by big-name Americans. The most appallingly bad painting, by Mark Rothko, was made when the artist was ill, and it looks it. Several Rothkos from the Mellon collection, on view near the entrance to this exhibition, will serve to refresh the eye.

But there is much that is splendid between the extremes at the beginning and end of this show. In the first room there are two 1907 Picassos, a curious, atypical work purchased from the Nelson Rockefeller collection, and another early cubist nude that was once kidnaped from artist-critic Roland Penrose, the signature cut out and mailed to him by the picture-nappers. The work was retrieved and re-signed by Picasso. The repair can still be seen.

Past a large and important Franz Marc and a strong Expressionist work by Karl Schmidt-Rottluff, one arrives at the glory of Thyssen's modern collection--a group of early abstract paintings from the second decade of this century by Kupka, Kandinsky, Moholy-Nagy and the recently rediscovered Russian avant-garde painters Gustav Klucis, Ilia Chashnik and El Lissitzky. The latter painting is the one that National Gallery director J. Carter Brown said he would most like to own.

The subject of "The City and Still Life"--a title that appears in the catalogue but nowhere in the gallery--is the wobbly rationale for the next room. It is filled with vibrant, museum-quality paintings by Leger, Braque, Gris, Weber, Kupka (a wonderful still-life of a machine going full-tilt), and two Feiningers that may well be among the finest paintings he ever made.

From there one moves down (literally and qualitatively) to the floor below where tacky surrealist paintings by Dali and Delvaux are forgiven only by the presence of George Grosz' spellbinding "Metropolis," an apocalyptic vision of Europe on the verge of falling apart between 1911 and 1917. Probably painted while the artist was on leave from the German army in Berlin during World War I, the painting, incredibly, includes an unfurled American flag--Grosz' view of where the future lay and where he eventually emigrated. Two Chagalls round out this incongruous room.

The next gallery, which includes mediocre examples by O'Keeffe and other contemporary Americans, also reflects another of the collection's strengths--pre-World War II American art. There are two Hoppers--including the large "Hotel Room" which stood out even in the context of Hopper's recent Whitney retrospective--and a wonderful little Stuart Davis oil and watercolor. There is also a striking work by photo-realist Richard Estes titled "Telephone Booth."

The final room suggests a real passion for certain Europeans who live, or lived, in England, notably the late Stanley Spencer, R.B. Kitaj, Francis Bacon and Lucien Freud, grandson of Sigmund--an artist well-known in Europe but rarely seen here. Though the spooky Freud on view does not reflect his more interesting, meticulous realist style, it could whet American appetites for a larger show of his work. Unfortunately, Freud's portrait of the baron was completed too late to be included in this show.

If one leaves this exhibition somewhat disappointed, it may have more to do with its structure than with the collection itself. Being the peerless art historian he is, Lieberman has chosen to present these paintings as a mini-history of 20th-century masters and trends, and therein lies its flaw. The baron says that he buys "personally and intuitively, not categorically," and the paintings might better have been presented in this more modest spirit. A show of the baron's best paintings--chosen by him--might have been more revealing.

As it is, the whole enterprise--particularly the catalogue on which the exhibition is based--has the sense of being overblown, of presenting the history of modern art through the pinhole lens of the Thyssen collection, and thus distorting the collection into something it was never intended to be--a history of 20th-century art.

But it remains, even with its faults, one of the finest modern collections in the world, according to Lieberman. He says that only the Museum of Modern Art in New York can rival the baron's holdings in the Russian Avant-Garde. "It's a very young collection," he says, "and the baron continues to collect with dazzling rapidity." Asked whether Thyssen's collecting style recalled that of the late Joe Hirshhorn, Lieberman replied that the baron "does not buy in gaggles."

And what is likely to become of the collection? The baron says he will probably not attach a wing to the Villa Favorita in Lugano to house the modern collection. "Too much in one place," he says. Could it come to America? "America? That's possible," though he didn't say where. The race is on.

Several future loan exhibitions of still unseen portions of Thyssen's holdings are in the works, however, most notably a show of 18th- to 20th-century American paintings. It is scheduled to open at the Vatican in fall 1983 and to subsequently tour Europe and America.

After the present exhibition leaves Washington Sept. 6, it will, like the old masters show, tour American museums under the auspices of the International Exhibitions Foundation. Hartford, Toledo, Seattle, San Francisco and the Metropolitan Museum in New York will host the show. United Technologies has spent close to $1 million to underwrite the two Thyssen exhibition tours. Asked whether it had an art collection of its own, an official of the company said no, but that a decorator had covered the walls of the new building in Hartford "with something."

Rich or poor, it's nice to have money.