The structural transformations occurring in fibers of syndiotactic polypropylene (sPP) during stretching have been studied by wide-angle X-ray diffraction measurements, using syncrotron radiation. sPP samples were cyclically stretched and relaxed at controlled rate, while recording X-ray fiber diffraction patterns and stress-strain curves. Clear evidences that the polymorphic transition between the helical form II and the trans-planar form III of sPP is a fast process and occurs on the same time scale as the rate the material is stretched, are provided. The transition of form II into form III starts during the stretching in correspondence to critical values of the stress-strain parameters. As the strain increases, crystals of form 11 transform into form III and the inverse transition occurs, releasing the tension. Below a critical strain, the sample is almost completely in the helical form, as in the initial unstrained state. A complete recovery of the initial dimensions of the specimen is observed, upon releasing the tension. Moreover, the total amount of crystallinity does not change during cyclic elengation and recovery. This suggests that the reversible phase transition between form II and form III does not involve the formation of any disordered, intermediate phase, i.e., it is a direct and cooperative process, implying conformational and structural rearrangements of large bundles of close neighboring chains and occurs instantaneously. These data indicate that while the driving force leading the conventional elastomers to recover the initial dimensions is merely entropic, in the case of sPP elasticity is also assisted by the enthalpic gain achieved when the sample is relaxed. When the tension is removed, both the enthalpic factor, due to the structural transition in the crystalline region, and an entropic factor, due to the conformational transition of the chains in the entangled amorphous phase, contribute to the elastic recovery of the fiber. A possible mechanism for the martensitic crystal-crystal phase transition of sPP is suggested.