Herein we present a system to obtain fibers from clickable elastin-like recombinamers (ELRs) that crosslink in situ during the electrospinning process itself, with no need for any further treatment to stabilize them. These ELR-click fibers are completely stable under in vitro conditions. A wrinkled fiber morphology is obtained. In addition to a random fiber orientation, oriented fibers with a high degree of alignment and coherence can also be obtained by using a rotational electrode. The production of multicomponent fibers means that different functionalities, such as cell-adhesion domains (RGD peptides), can be incorporated into them. In a subsequent study, two main cell lines present in the dermis and epidermis, namely keratinocytes and fibroblasts, were cultured on top of the ELR-click fibers. Adhesion, proliferation, fluorescence, immunostaining and histology studies showed the cytocompatibility of these scaffolds, thus suggesting their possible use for wound dressings in skin tissue engineering applications.