From 1986 to 2003 he worked in the Department of Zoology at Tel Aviv University. He retired in 2006 as Norman and Rose Lederer Professor Emeritus of Zoology. In 2003, he moved to the University of Houston. From 2009 to 2011 he has held the position of Councillor for the Society for Molecular Biology and Evolution. Graur has been noted for his criticisms of the ENCODE project.[5]