| Orthostichidium quadrangulare (Schwägr.) B.H. Allen & Magill, 2007 |
| Orthostichidium tetragonum (Sw. ex Hedw.) Müll. Hal., 1897 |
| Orthostichopsis Broth., 1906 |
| Orthostichopsis tetragona (Hedw.) Broth., 1906 |
| Pirea Cardot, 1893 |
| Pirea mariae Cardot, 1894 |
| Pirea pachyclada Renauld & Cardot, 1905 |
| Pireella Cardot, 1913 |
| Pireella cymbifolia (Sull.) Cardot, 1913 |
| Pireella denticulata Cardot & Thér., 1940 |
| Pireella guatemalensis E.B. Bartram, 1946 |
| Pireella guatemalensis var. mexicana Arzeni, 1954 |
| Pireella mariae (Cardot) Cardot, 1913 |
| Pireella pachyclada (Renauld & Cardot) Cardot, 1913 |
| Pireella pohlii (Schwägr.) Cardot, 1913 |
| Pireella pycnothallodes (Müll. Hal.) M. Fleisch., 1917 |
| Pterobryaceae Kindb., 1896 |
| Pterobryon Hornsch., 1840 |
| Pterobryon cymbifolium (Sull.) Mitt., 1864 |
| Pterobryon densum (Hornsch.) Hornsch., 1840 |