The two volumes LNCS 9107 and 9108 constitute the proceedings of the International Work-Conference on the Interplay Between Natural and Artificial Computation, IWINAC 2015, held in Elche, Spain, in June 2015. The total of 103 contributions was carefully reviewed and selected from 190 submissions during two rounds of reviewing and improvement. The papers are organized in two volumes, one on artificial computation and biology and medicine, addressing topics such as computational neuroscience, neural coding and neuro-informatics, as well as computational foundations and approaches to the study of cognition. The second volume deals with bioinspired computation in artificial systems; topics alluded are bio-inspired circuits and mechanisms, bioinspired programming strategies, and bioinspired engineering AI&KE.