Keldysh was a member of many foreign academies of sciences, including the Mongolian Academy of Sciences (1961), Polish Academy of Sciences (1962), Czechoslovak Academy of Sciences (1962), and Romanian Academy of Sciences (1965). He was also an honorary member of the American Academy of Arts and Sciences (1966), Bulgarian Academy of Sciences (1966), Hungarian Academy of Sciences (1970), and Royal Society of Edinburgh (1968), foreign corresponding member of the German Academy of Sciences (1966), and Saxon Academy of Sciences in Leipzig (1966).