Acroporidae Verrill, 1901 (additional source)
Actinastraeidae Alloiteau, 1952 † accepted as Actinastreidae Alloiteau, 1952 † (basis of record)
Agariciidae Gray, 1847 (additional source)
Agathiphylliidae Vaughan & Wells, 1943 † (additional source)
Amphiastraeidae Alloiteau, 1952 † (basis of record)
Andemantastraeidae Alloiteau, 1952 † (additional source)
Coryphylliidae Beauvais, 1981 † (original description)
Cyathophoridae Vaughan & Wells, 1943 † (basis of record)
Dermosmiliidae Koby, 1889 † (basis of record)
Ellipsosmiliidae Alloiteau, 1957 † (basis of record)
Faviidae Milne Edwards & Haime, 1857 (additional source)
Funginellidae Alloiteau, 1952 † accepted as Fungiidae Dana, 1846 (basis of record)
Latomaeandridae Alloiteau, 1952 † (basis of record)
Montlivaltiidae Dietrich, 1926 † accepted as Thecosmiliidae Duncan, 1884 † (basis of record)
Procyclolitidae Vaughan & Wells, 1943 † (basis of record)
Stylinidae d'Orbigny, 1851 † (additional source)
Stylophyllidae Frech, 1890 † (additional source)
Synastraeidae Alloiteau, 1952 † (additional source)
Thamnasteriidae Vaughan & Wells, 1943 † (additional source)
Tropiphyllidae Beauvais, 1981 † (original description)