OLD MASTER Paintings from the Collection of the Baron Thyseen-Bornemisza" is a grand, old-fashioned picture show. The Baron's precious paintings are badges of his class.

The finest works displayed here -- the Carpaccio, the Heemskerck, the Antonello da Messina -- seem, at least at first, wholly unconnected. But as one confronts them, they begin to act together, to conjure up a vanished world of palaces and princes. The grandeur intimidates; the privilege amazes. Forming this collection seems scarcely possible in the present age. Seen together, the 57 pictures partake of ghostly theater; they seem the ornaments of dreams.

Everbyody knows that if you want to buy Old Masters now, you might as well forget it. The best ones aren't for sale; they're already in museums. But the Baron Thyssen-Bornemisza does not seem to understand that. The Baron singlehandedly competes with wealthy nations and with great museums. His eye is sharp, his fortune large, his ambition even larger. He buys and buys and buys.

The pictures he has sent us -- his Rembrandt and his Rubens, his van Eycks and his Goyas, his Duccio and his Fragonard -- are without exception old. But his collection isn't. Two-thirds of the Old Masters here have entered his collection since the end of World War II.

He bought his Rembrandt from Lord Margadlae in 1976, his Lucas van Leyden from Lady Dunsany in 1971, and his little Petrus Christus, a jewel of a picture, from the late Konrad Adenauer in 1965.Few of us will ever meet a man so well-connected. He bought his Duccio from the collection of John D. Rockefeller II in 1971, his imposing Palma Vecchio from Baron Edouard de Rothschild in 1959, and his luscious Fragonard from Baron Maurice de Rothschild in 1956. The Prince of Lichtenstein once owned the baron's Canalettos, his Juan de Flkandes "Pieta" came from the Duc de Blacas in 1956. And his extraordinary Heemskerck, a Portrait of a Lady With a Spindle and a Distaff," was acquired, a decade ago, form the Earl of Caledon.

"Except for the Royal Collection inherited by the Queen of England," writes John Walker, the National Gallery's director emeritus, "the Thyssen-Bornemisza Collection is now the greatest private collection in the world."

The mood of antique grandeur carried by these paintings has been subtly enhanced by the way the've been installed. The Baron's pictures hang on two floors of the East Building, so that halfway through the show the display is interrupted while the viewer climbs a curving, skylit stair. Old-fashioned fluted moldings have been added to the walls. The softly diffused daylight, the thickness of the carpet, the gracious spiral stair and the colors of the walls allow one to forget that one is looking at these paintings in a public institution. Gil Ravenel's installation quitetly suggests the luxyury, the hush, of some great private house.

The Baaron's taste, it should be said, is difficult to fault. His Dutch still-lifes are wondrous. In one by Willem Kalf (1919-1693), a beam of sunlight, piercing through the shodows, casts its sudden light on a crumpled Persian rug, a lemon peel and a Chinese bowl. It is described by Allen Rosenbaum, the Princeton art historian who wrote the exhibition's catalog, as "the finest of Kalf's pronkstilleven , or luxurious still lifes (pronk meaning 'show' or 'ostentation.')" Once in the collection of Count Alexis Orioff Davidoff, the Kalf was purchased by the Baron in 1962. The "Still Life with Flowers" by Jan Davidsz de Heem (1606-1683) is equally compelling. The peonies, striped tulips and cherry blossoms shown seem moist and garden-fresh. In addition, the picture is a can-you-find-the-animals? entertainment. A dozen lively bugs, butterflies and snails crawl upon its blooms.

Handsome as his still-lifes are, the Baron's portraits are even more impressive.

The grandest without doubt is the the brilliant, life-size image of a "Young Knight in a Landscape (Francesco Maria della Rovere, Duke of Urbino,)" painted by Carpaccio in 1510. Viewers might spend hours, and scholars might spend years, studying the details most of them symbolic, of this extraordinary painting. All its elements -- its dogs and frogs and many birds, its stag -- seem locked into postion. "Rovere" means oak, and the work is full of oak trees. The young knight's armor gleams, his shoes are checked chain mail, and he seems to have a folded note tucked into his codpiece. One suspects that curators would kill to own this painting. It once was in America, in the New York collection of the late Otto M. Kahn. The Baron's father bought it in 1934.

Antonello da Messina's "Portrait of a Man," though far smaller and far simpler, seems nearly perfect. Christopher Amberger's painting of Mattheus Schwartz (and of his sitter's horoscope), Jan Steen's portrait of himself (plucking a lute and grinning at the Viewer), Fiovanni Battista Piazetta's portrait of his heavy-lidded colleague, the woman painter Giula Lama, the Palma Vecchio, the Memling, the Rembrandt and the Goyas -- all these are works of high distinction. Despite such competition, Heemskerck'sdark-eyed spinning lady is as notable a portrait as any in the show.

Of the Boran's 18th-century French paintings, the Boucher and the Fragonard are the most seductive. Boucher's saucy beauty is flashing just a bit of thigh as she ties on her garter. Fragonard's is riding on a seesaw. (His subjects may be frivolous, but how that man could paint.)

Of the religous pictures shown, the tiny Petrus Christus and the twin van Eycks are perhaps the most peculiar. Mary and the angel in the two trompe l'oeil van Eycks seem living statures made of stone, not flesh. The Petrus Christus, "Our Lady of the Barren Tree." portrays the Madonna ringed by a crown of throns; 15 gleaming golden "a"s hang from its pointed spikes. (The "a"s might stand for ave, as in Ave Maria, which Medieval theologians regarded as the reverse of the name of fallen eve. )

Though the two works by El Greco here strike me as unbeautiful -- and though the finest paintings shown subordinate the lesser ones -- this collection is so good that almost every picture rewards contemplation. It is odd what details one carries from this show; the strangely homely face of the Bernhard Strigel andgel, Pieter de Hooch's patient dog, Heda's shattered glass, Heemskerck's ornate spinning wheel, Carpaccio's plashing fountain. One leaves his the baron.

The International Exhibitions Foundation of Washington's Annemarie H. Pope, aided by a grant from the United Teahnologies corp., organized the show. It will remain on view here through Fed. 17.