There are, in _Gryllus_ spermatids, two quite permanent and prominent extra-nuclear bodies. The larger of these I shall call _nebenkern_, because I believe it originates from the spindle remains, and goes to form the tail covering. Its behavior is as follows: At the beginning of the telophase the fibers which had connected the centrosomes with the chromosomes bulge out like barrel staves, as Henking (’91) has described. These break loose from the chromosomes and centrosomes as the clear space begins to form around the chromatin mass (fig. 2); but they are not separated into two rings, as in _Anasa_ and _Pyrrhocoris_. As the dividing cell membrane is formed, the middle portions of the fibers are drawn together and the so-called “mid-body” is formed. Some of the fibers unite, producing thicker ones, as seen in figs. 1, 2, and 3. In the last-named figure some of the central fibers seem to be still united with those of the companion spermatids. As the daughter-cell shortens and the nucleus takes a more central position these fibers unite still more, shorten, bend together (figs. 4, 5, and 6), and finally assume the shape shown in fig. 7. I shall call it for the present the “striated condition,” or simply “striated nebenkern.” The shape resembles that of an egg with rather sharply drawn-out ends. The surface is occupied at intervals with deeply staining lines which look much like hoops. In most cases the long axis of the nebenkern is at right angles to the axis of the spindle from which it was formed, while the striæ, or dark lines, are in planes parallel to it, as is seen in figs. 7 and 8_a_. In a few cases the lines are parallel to the long axis of the nebenkern, as shown in fig. 8_b_. Fig. 9 exhibits a partial end view of the nebenkern, while fig. 26 represents a polar view in all planes. The fibers in figs. 4 and 5 are not all in the same plane, giving frequently, with changing focus, the impression that the lines are the edges of plates. Even in figs. 7 and 8, the appearances shown made me hesitate for some time before I dared say that the lines represent striæ on the surface and not plates extending through the body. But the end views (figs. 9 and 26) and the two drawings in fig. 19 show clearly that we are dealing with encircling hoops and not dividing plates. Just how or why the fibers bend and assume the shape of figs. 7 and 8 I am not able to say, but I am sure it is not an artefact, as might be supposed, because I have found them occupying whole cysts of several testes, and nearly all of them were as regular and definite as fig. 7.[A]