The neurological explanation of consciousness has become in the last decades a widespread field of research among neurobiologists and philosophers of mind. The development of experimental models of consciousness involves a parallel search for a suitable ontological background. Although most researchers share anti-dualistic and naturalistic ideas, there are controversial claims about the ontological interpretation of phenomenological data. After sketching some historical premises of this issue, the paper focuses on two case studies: Dennett's "multi-draft" model of consciousness, and Edelman's theory of consciousness, included in his "theory of the selection of neuronal groups". Edelman's theory turns out to provide a better solution to the open issues of contemporary research, since it avoids speculative hypotheses and dismissive attitudes, while leaving room for experimental and conceptual developments in a classical, "Newtonian" methodological style.