In-situ structural evolution during uniaxial extension and subsequent retraction of a thermoplastic elastomer (TPE) based on propylene-dominant ethylene-propylene (EP) copolymer was studied. Combined measurements of time-resolved wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) as well as stress-strain curves revealed molecular mechanism responsible for the elastic behavior. During the first cycle of deformation, a fraction of the crystals was destroyed, while the rest was reoriented. At strains larger than 1.0, strain-induced alpha-crystals in the lamellar form took place, resulting in the creation of a network with well-oriented lamellae having their normals parallel to the stretching direction. With the increase of strain, more crystals were induced, forming an enhanced network with strain-hardening behavior. During retraction and even after complete relaxation to zero stress, the majority of the strain-induced crystalline network remains in tact as being "permanent set", where lamellar stacks act as the network points. This strain-induced crystalline network structure is thermally stable at room temperature and is responsible for the elastic behavior during subsequent cyclic deformation, similar to a vulcanized rubber.