This chapter seeks to articulate some necessary steps towards a linking hypothesis between two levels of analysis that are central for any integrative attempt of the sort that animates the biolinguistic enterprise: the “cognome” and the “dynome”, or more generally, the mind and the brain. Unlike previous work seeking to bridge the gap between mind and brain, we develop an approach that is not merely locationist but seeks to ground aspects of linguistic knowledge, including syntactic principles of our language faculty, and processing onto basic neurophysiological principles. The key notion behind the suggested linking hypothesis rhythm. At the level of the cognome, rhythm is intrinsically related to the better known notion of cyclicity. At the level of the dynome, rhythm is investigated under the notion of brain oscillation. In both cases, the basic idea we will exploit is that rhythmic processes act as structuring principles.