In fibers spun from polymer solutions, we investigated self-organization of ordered shish kebabs via the cascade evolution of various dissipative structures through multistep phase transitions at multiple length scales. We used transmission electron microtomography to discover for the first time crystalline fibrils with diameters of similar to 10 nm that orthogonally bridge neighboring kebabs epitaxially overgrown from shishs. The fibrils evolved during the late-stage self-organization processes of the shish kebabs. The fibrils were classified as completely bridging fibrils and pairs of broken fibrils facing each other; the broken fibrils were formed by the following two steps, first by the flow-induced burst of the bridging domains driven by Laplace pressure and subsequent crystallization involved in the burst domains. The bridging and broken fibrils were observed at interkebab distances smaller and larger than the critical length of similar to 80 nm, respectively. The bridging fibrils and the cores of the broken fibrils had a single fringed micellar crystalline structure extending over the whole fibrils. We proposed a plausible model for the fibril formation based on a coupling of the two types of the phase transitions, viz., viscoelastic phase separation followed by crystallization in the polymer solution confined in the space between existing shishs and kebabs when the solution temperature is lowered owing to the shift of the solution toward downstream along the spinning line. The crystallization into the fibrils occurs in the relevant amorphous template first developed by the phase separation as in the case of the shish-kebab formation. We demonstrated that the self-organization of the bridging fibrils is an important part of the whole self-organization process of shish kebabs in the fiber spinning process.