A catastrophic terminal Triassic extinction event among terrestrial vertebrates is not supported by available evidence. The current model for such an extinction is based on at least eight weak or untenable assumptions: (1) a terminal Triassic extinction-inducing asteroid impact occurred, (2) a terminal Triassic synchronous mass extinction of terrestrial vertebrates occurred, (3) a concurrent terminal Triassic marine extinction occurred, (4) all terrestrial vertebrate families have similar diversities and ecologies, (5) changes in familial diversity can be gauged accurately from the known fossil record, (6) extinction of families can be compared through time without normalizing for changes in familial diversity through time, (7) extinction rates can be compared without normalizing for differing lengths of geologic stages, and (8) catastrophic mass extinctions do not select for small size. These assumptions have resulted in unsupportable and (or) erroneous conclusions. Carboniferous through Early Jurassic terrestrial vertebrate families mostly have evolution and extinction patterns unlike the vertebrate evolution and extinction patterns during the terminal Cretaceous event. Only the Serpukhovian (mid Carboniferous) extinction event shows strong analogy to the terminal Cretaceous event. Available data suggest no terminal Triassic extinction anomaly, but rather a prolonged and nearly steady decline in the global terrestrial vertebrate extinction rate throughout the Triassic and earliest Jurassic. ?? 1992.