In continuation of my earlier published Conspectus (MEYER 1973) and the general part of the critical revision of the Thlaspi-species of Europe, the Near East, and Africa (Meyer 1979) here I begin with the description of the genera in which the genus Thlaspi s.lat. has been divided by me. The genus Thlaspi L. s. str. remains with six species which can be grouped in three sections: sect. Thlaspi, Th. arvense L., Th. huetii BoiSS., Th. kochianum F. K. Mey.; sect. Carpoceras DC., Th. ceratocarpon (Pall.) Murray, and sect. Chaunothlaspi O. E. SCHULZ, Th. alliaceum L., Th. oliveri Engl.. These sections show as common features their growth as annual herbs, an acrotonous branching, and an edged resp. grooved stalk. Though the sections seem to be quite different in their fruit-shape, the pattern of the anatomy of their seed-coats is very similar and differs from all the other species formerly combined under Thlaspi. So the formerly huge genus Thlaspi L. was restricted to the remaining six species. Later on, molecular investigations of the subunits of Rubisco and chloroplast DNA restriction-site variation by K. Mummenhoff, M. Koch, and K. Zunk during the years 1991-1997 confirmed my concept of a restricted genus Thlaspi which does not show nearer relations to the other species formerly put to Thlaspi. Here the description of the characters and the distribution of the different Thlaspi-species is given. In later following parts the results of the investigations in the species put to Thlaspi until now which belong to other genera, will be given.