Отряд Атрипиды Order Atrypida Rzhonsnitskaia, 1960. Lower Ordovician–Upper Devonian.
В среднем палеозое шесть надсемейств в четырех подотрядах.
Superorder Anazygidina Copper, 1996. Lower Ordovician–upper Silurian.
Superfamily Anazygoidea Davidson, 1883. Lower Ordovician–upper Silurian.
Superorder Atrypidina Moore, 1952. Upper Ordovician–Upper Devonian.
Superfamily Atrypoidea Moore, 1952. Upper Ordovician–Upper Devonian.
Superfamily Punctatrypoidea Punctatrypoidea. lower Silurian–Lower Devonian.
Superorder Lissatrypidina Copper, 1996. ?Lower Ordovician, Upper Ordovician–Upper Devonian.
Superfamily Lissatrypoidea Twenhofel, 1914. ?Lower Ordovician, Upper Ordovician–Upper Devonian.
Superorder Davidsoniidina Copper, 1996. upper Silurian–Middle Devonian.
Superfamily Davidsonioidea King, 1850. upper Silurian–Middle Devonian.
Superfamily Palaferelloidea Spriestersbach, 1942. upper Silurian–Middle Devonian.