Tissue engineering investigates new therapeutic approaches for spinal cord regeneration. Biodegradable scaffolds are employed aiming at creating an appropriate environment to support cell regrowth and transplantation. The transplantation of neural stem/progenitor cells (NSPCs) is a promising strategy under investigation. The main objective of this work was the synthesis of new soft materials for the production of nanostructured scaffolds able to support NSPCs transplantation and enable spinal cord regeneration. Polyurethanes (PUs) are segmented polymers, with tunable properties. PUs were synthesized using polycaprolactone-diol (PCL-diol) as soft segment, and isophorone diisocyanate and dimethylol propionic acid (DMPA) as hard segment. To introduce biological cues in the polymer backbone, chitosan (CS) and gelatin (Gel) were used to substitute DMPA as chain extender. The PUs were characterized regarding their chemical composition and thermal properties. Electrospun fibrous mats are convenient structures for cell support. In particular, aligned nanofibers provide a guidance cue to axon regrowth. Electrospinning was used to produce scaffolds of randomly oriented and aligned fibers from the different PU formulations. Scaffolds were characterized regarding their morphology, mechanical behavior, crystallinity, surface properties and hydrolytic degradation. Their impact on cells was evaluated in vitro using human fibroblasts. Cell adhesion and proliferation was highest for scaffolds produced from PUs containing CS or Gel as the only chain extender. Stem cell interaction with PU-CS and PU-Gel scaffolds was studied using human umbilical cord mesenchymal stem cells (MSCs) and human fetal spinal cord neural stem cells (NSCs). MSCs proliferated best on PU-Gel randomly oriented fibers whereas NSCs proliferated best on PU-CS with aligned fiber morphology. Neuronal differentiation of NSCs was confirmed using neuronal markers. Neurites aligned along the fibers direction. The physical, chemical and biological properties of PU-CS and PU-Gel fibrous mats make them promising substrates for NSPC in order to promote neural regeneration.