Hörmander mostly remained at Lund University as professor after 1968, but made several visits to the United States during the two next decades. He visited the Courant Institute in 1970, and also the Institute for Advanced Study in 1971 and during the academic year 1977–1978 when a special year in microlocal analysis was held. He also visited Stanford in 1971, 1977 and 1982, and the University of California, San Diego in the winter 1990. He was briefly director of the Mittag-Leffler Institute in Stockholm between 1984 and 1986, but only accepted a two-year appointment as he "suspected that the administrative duties would not agree well" with him, and found that "the hunch was right". He also served as vice president of the International Mathematical Union between 1987 and 1990. Hörmander retired emeritus in Lund in January 1996. In 2006 he was honored with the Leroy P. Steele Prize from the American Mathematical Society.