| Honer, Chris | Chris Honer | Director | 2011 | 1 | |
| Heiberg, Johanne Luise | Johanne Luise Heiberg | Director | 1870 | 2 | 2 |
| Heiberg, Gunnar | Gunnar Heiberg | Director | 1885 - 1918 | 9 | 1 |
| Heinrich, Wilhelm Ernst | Wilhelm Ernst Heinrich | Director | 1889 - 1901 | 6 | |
| Harding, Jessie | Jessie Harding | Director | 1895 | 1 | |
| Heine, Dr. Carl | Carl Heine (Dr. Carl Heine) | Director | 1896 - 1918 | 54 | 1 |
| Hagin, Heinrich | Heinrich Hagin | Director | 1903 - 1904 | 2 | |
| Hagemann, Carl | Carl Hagemann | Director | 1910 - 1911 | 2 | |
| Heller-Halberg, Friedrich | Friedrich Heller-Halberg | Director | 1912 | 1 | |
| Hellmer, Arthur | Arthur Hellmer | Director | 1914 - 1915 | 2 | |
| Herbert, Eugen | Eugen Herbert | Director | 1923 | 1 | |
| Held, Ernst | Ernst Held | Director | 1927 | 1 | |
| Hartung, Gustav | Gustav Hartung | Director | 1932 | 1 | |
| Henze, Herbert | Herbert Henze | Director | 1936 - 1938 | 2 | |
| Heinle, Lutz | Lutz Heinle | Director | 1941 | 1 | |
| Haufe, Heinz | Heinz Haufe | Director | 1942 | 1 | |
| Hahn, Erwin | Erwin Hahn | Director | 1929 - 1947 | 2 | |
| Hedberg, Karl | Karl Hedberg | Director | 1901 - 1918 | 5 | |
| Heiberg, Anton | Anton Heiberg | Director | 1905 - 1907 | 2 | |
| Høegh, Thomas | Thomas Høegh | Director | 1991 - 2009 | 12 | 1 |
| Hedemann, Berit | Berit Hedemann | Director | 1992 | 1 | 1 |
| Hellesøy, Svein | Svein Hellesøy | Director | 2002 | 1 | |
| Heijermans, Herman | Herman Heijermans | Director | 1916 - 1918 | 2 | |
| Hofman, Jerži | Jerži Hofman | Director | 1970 | 1 | |
| Hiatt, Bernard | Bernard Hiatt | Director | 1977 | 1 | |
| Hasnain, Arif | Arif Hasnain | Director | 1977 | 1 | 1 |
| Holt, Louise | Louise Holt | Director | 1928 | 1 | |
| Haspel, Dieter | Dieter Haspel | Director | 1975 - 1983 | 2 | |
| Hornby, Richard | Richard Hornby | Director | 1975 | 1 | 1 |
| Hjelm, Fred | Fred Hjelm | Director | 1974 - 1990 | 3 | 1 |
| Hopkins, Bernard | Bernard Hopkins | Director | 1978 - 1990 | 2 | |
| Haugen, Ralph | Ralph Haugen | Director | 1951 - 1972 | 3 | |
| Hancke, Oswald | Oswald Hancke | Director | 1898 | 1 | |
| Hussein, Waris | Waris Hussein | Director | 1972 | 1 | |
| Hoomans, Elise | Elise Hoomans | Director | 1979 | 1 | |
| Hahn, Georg | Georg Hahn | Director | 1973 | 1 | |
| Hahn, Annegret | Annegret Hahn | Director | 1979 | 1 | |
| Höller, Konrad | Konrad Höller | Director | 1973 | 1 | |
| Haid, Franz | Franz Haid | Director | 1902 | 1 | |
| Haoyi, Huang | Huang Haoyi | Director | 1985 | 1 | |
| Hammond, David | David Hammond | Director | 1983 | 1 | 1 |
| Hayes, William | William Hayes | Director | 2009 | 1 | |
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