[KALKI]

Dr. Gordon F. Ekholm, curator emeritus of anthropology at the American Museum of Natural History and an authority on pre-Columbian archeology of Mexico and Central America, died Thursday at the Phelps Memorial Hospital Center in Tarrytown, N.Y., after undergoing minor surgery. He was 78 years old and lived in Pleasantville, N.Y.

In 1949, Dr. Ekholm displayed at the museum a graphic and detailed exhibition showing parallels between advanced cultures in southern and eastern Asia and the Mayan civilization, which flowered between 300 and 900, and suggesting that the Mayans' forebears had migrated across the Pacific. The theory was a major focus of his career.

Dr. Ekholm was born in St. Paul. He was an alumnus of the University of Minnesota and did extensive graduate studies in anthropology at Harvard University, where he earned master's and doctoral degrees. Expeditions to Meso-America

He joined the staff of the museum, on Central Park West at 78th Street, in 1937, became an assistant curator in 1942, an associate curator in 1947 and curator in 1957.

He also participated in and headed many digging expeditions in Mexico, Guatemala, Honduras and the former British Honduras, now Belize.

After retiring in 1974, he became curator emeritus and continued consulting on museum projects.

As curator, Dr. Ekholm organized the permanent installation of the Hall of Mexico and Central America in 1970. Hailing the institution as ''one of our first art museums,'' John Canaday, an art critic of The New York Times, described the exhibition as ''a gem in the crown of this installation in its 100th anniversary year.'' Challenges to Authenticity

The catalogue for the exhibition was written by Dr. Ekholm. Mr. Canaday termed the publication ''as clear and concise an introduction to Meso-American archeology as you are likely to find anywhere.'' He added that ''the magnificent'' stone and ceramic sculptures in the hall ''triumphantly declare their own identity as works of art, and surely they must constitute one of the two or three finest pre-Columbian collections'' outside Mexico City.

Dr. Ekholm was also known for challenging the authenticity of questionable pre-Columbian works. The field attracts very high prices and, as a result, many sophisticated forgers.

He was president of the Society for American Archeology from 1953 to 1954 and of the Institute of Andean Research from 1968 to 1971. Dr. Ekholm lectured on Mexican and Mayan archeology at Columbia University from 1943 to 1971, and he had been a consultant for the Museum of Primitive Arts since 1958.

Surviving are his wife, the former Marguerite Wander, who accompanied him on many expeditions and aided him at the museum as a volunteer; a daughter, Suzanna, an archeologist in Chiapas, Mexico; a son, Erik, of North Whitefield, Me., and two grandchildren.