From the beginning of the anthropology of *kinship, the systems known as ‘CrowOmaha’ have been rich sources of debate. Discovered by *L.H. Morgan (1871), they are characterized by a distinctive type of *relationship terminology with little respect for genealogical levels. Interpretation of these terminologies has varied as different schools of anthropology have come and gone. For *descent theory (principally British and †Durkheimian), they constitute an extreme type of †unilinearity. For *alliance theory (chiefly French and †Maussian), they correspond to *marriage systems founded on numerous marital prohibitions. For American formalism, they obey a classificatory logic which operates through †extension of some kin terms for some authors or through reduction for others. Other interpretations are also advanced now.