Efim Isaakovich Zelmanov (born September 7, 1955) is a mathematician, known for his work on combinatorial problems in nonassociative algebra and group theory, including his solution of the restricted Burnside problem. He was awarded a Fields Medal in 1994.

He was born into a Jewish family in Khabarovsk in Russia, at that time in the USSR. He took a doctoral degree at Novosibirsk University, and a higher degree at Leningrad State University in 1985. He had a position in Novosibirsk until 1987, when he left the Soviet Union.

From 1990 he was professor at the University of Wisconsin-Madison; he was at the University of Chicago in 1994/5, then at Yale University.

As of 2004, he is professor at the University of California, San Diego.

His early work was on Jordan algebras in the case of infinite dimensions. He was able to show that Glennie's identity in a certain sense generates all identities that hold. He then showed that the Engel identity for Lie algebras implies nilpotence, in the case of infinite dimensions.