1. After reviewing current theories on the origin of the pteridosperm ovule it is concluded that only one, the telomic concept, can account for all the structural variations found within the group.
2. It is therefore suggested that in at least most cases the pteridosperm ovule evolved by the enclosure of a terminal sporangium within an integument derived from a number of adjacent branches or telomes.
3. A cupule or second integument, often enclosing more than one ovule, later evolved by a similar process.
4. The available evidence suggests that both integument and cupule evolved independently a number of times and that consequently the ovule itself must have arisen several times in the pteridosperms.
5. Since the possession of an ovule is the one important feature common to the whole group, this implies that the pteridosperms must have had a polyphyletic origin.
6. It is suggested that Cordaitalean ovules are primarily radially symmetrical, having a first integument derived from several telomes, and that they became bilaterally symmetrical with the evolution of a second integument derived from only two telomes.
7. Evidence provided by the ovule supports the view that the Cordaitales are monophyletic.
8. There is no foundation for the view that the ovulate organs of the Cordaitales are stachyosporous. The same is probably true of the pteridosperms.
9. Evidence of a direct relationship between the pteridosperms and the Cordaitales is inconclusive.