1. In the vascular system of the Hymenophyllaceae and of the Schizaeaceae the same characteristic features are seen as in other groups of Ferns. 2. In the Hymenophyllaceae the reduction of the adaxial metaxylem of the leaf-trace never reaches the xylem of the stem, which is often reduced in its own way. 3. In the Schizaeceae all grades of development may be observed but pith is never formed independently of the parenchyma of the leaf-trace. 4. The distinction between leaf-trace xylem and stem xylem is justified from a descriptive point of view; whether one of them is derived from the other, cannot be decided owing to lack of evidence. 5. Some theories of Lignier agree with views, formerly given.