An enhanced elasticity of electrospun fibers while retaining their strength would be of great benefit for a set of applications (including tissue engineering). One route toward enhanced elasticity may be based on the introduction of curvature, i.e., of buckled or tight nanocoil (nanospring) configurations. The concept investigated in this contribution is to introduce such configurations via a differential shrinkage of a parallel arrangement of a flexible thermoplastic elastomer (polyurethane) component and a rigid thermoplastic component. Core-shell fibers are produced for this purpose by coaxial electrospinning. It is observed that buckling-nanospring formation can be achieved in this way. The morphology of such fibers and also modifications in the conductivity of the spinning solutions have a considerable effect on details of buckling and nanospring formation.