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In this paper, we discuss computational architectures that are motivated by connectionist patterns that occur in biochemical networks, and speculate about how this biochemical approach to connectionism might complement conventional neural approaches. In particular, we focus on three features of biochemical networks that make them distinct from neural networks: their diverse, complex nodal processes, their emergent organisation, and the dynamical behaviours that result from higher-order, self-modifying processes. We also consider the growing use of evolutionary algorithms in the design of connectionist systems, noting how this enables us to explore a wider range of connectionist architectures, and how the close relationship between biochemical networks and biological evolution can guide us in this endeavour.