Willem de Kooning's "Two Women" tonight was sold for $1.98 million, a record for a contemporary work of art and for a living artist. The 1953 oil on paper was the top sale at the Christie's auction, which also set a record of $6.9 million for contemporary art.

A spokesman for the auction house declined to name the buyer or seller of the de Kooning work.

Among the major American abstract expressionist artists, Dutch-born de Kooning, 80, who lives and works in East Hampton, Long Island, is considered by many second only to the late Jackson Pollock. Two years ago, a painting from de Kooning's "two women" series broke the million-dollar mark, going to the Australian national museum for $1.2 million. The work sold tonight has been particularly sought after because the figures in it are defined, unlike the artist's later women pictures.

Tonight's auction was the second and final round of sales of post-World War II art here in New York. Unlike Wednesday night's sale at Sotheby's, tonight's sale offered more masterpieces than usually appear on the open market. The prices reflected the difference. At Sotheby's, 80 lots were knocked down for $4.9 million. Tonight, the same number of pieces brought $2 million more.

The trends remained the same. High bids were placed for works of great quality by leading figures of the 1950s and 1960s, and new interest in minimalist and Pop Art was noted, but very recent works by young artists proved disappointing. Robert Motherwell's "Wall Painting No. III" (1953), which failed to sell during a market slump two years ago, brought bidders to their feet this time and fetched $275,000. Its buyer was not named. Sam Francis' "Towards Disappearance" (1957-1958), was sold for a record $770,000 to records producer David Geffen. Adolph Gottlieb's "Apaquoge" (1961), from the collection of Mary Lasker, was sold for $240,000 to E.A. Carmean, on behalf of the Fort Worth Museum of Art. Washington dealer Chris Middendorf walked away with an early Jackson Pollock, "The Magic Mirror" (1941), for $374,000.

Washington color school artists were not represented by any major pictures. What was here, however, sold well. A Morris Louis stripe, "Blue Column" (1961) sold for $33,000. Another stripe, "Infield" (1962) brought $110,000 and a third stripe, "Unit" (1962), went for $55,000. "Twin Plane" (1967), by Kenneth Noland, was sold for $19,800.

David Hockney, who was represented at Sotheby's with four record-breaking pictures, fared well again tonight. The British artist's "Seated Woman Drinking Tea, Being Served by Standing Companion" (1963), the same vintage as Wednesday night's "Play Within a Play," also influenced by the work of 17th-century Italian artist Domenichino, brought $220,000.

George Segal led the pop artists with "The Laundromat," which sold for $77,000. Claes Oldenburg's "Giant Soft Swedish Light Switches" (1966) was sold for $55,000. A life-size and realistic cast of a policeman striking a black protester with his billy club by Dwayne Hanson, titled "Riot" (1967), brought $46,200.

A new record high was also set for minimalist Robert Mangold. His "Circle Painting #4" (1973), first exhibited at the Max Protech gallery in Washington, brought $21,000. A record was also set for Sol Lewitt, whose "Sculpture Serial Project A-1/0" (1966) sold for $14,300.

With more than 500 persons crowded into the main Park Avenue salesroom, there was excitement -- and some confusion -- over the bids. Bidding was steady and brisk, and the main battle of the evening took place for the de Kooning.

As nearly everyone in the room sat stock-still, David Bathurst, the auctioneer and president of Christie's, began the bidding at $100,000. The bids inched up in hundred-thousand-dollar increments to the closing $1.98 million.

The anonymous buyer made the winning bid by telephone.

The sale concluded with a disappointing showing from works by young artists. "Brutes as Protagonists of a Monkey's Erotic Fantasy" (1979) by the Italian Sandro Chia failed to sell, though bidding reached $28,000. Also failing to sell was "Noch ist Polen Verloren VI" (1978) by German neo-expressionist Ansem Keifer; not a single bid was placed for an oil on velvet by Julian Schnabel titled "Dream" (1983).