Accumulated phytochemical data partially compiled by Kubitzki in 1969, and evidence from various other sources point to a fundamental heterogeneity of the Flowering Plants, which is interpreted by the present author as an unmistakable indication of a multiple descent of the Angiosperms. The consequences of this viewpoint for taxonomic classifications and for phylogenetic speculations must be faced. In view of the possible misunderstanding of some pointers, and in order to avoid erroneous interpretations of the accumulated evidence, a survey of the relevant data appears to be indicated. Some tentative proposals concerning a future classification of the Angiosperms will be made in the second part of this paper.