The molecular basis of many forms of signal transfer in living organisms is provided via the transient phosphorylation of regulatory proteins by transfer of phosphoryl groups between these proteins. The dominant form of signal transduction in prokaryotic microorganisms proceeds via so-called two-component regulatory systems. These systems constitute phosphoryl transfer pathways, consisting of two or more components. Most of these pathways are linear, but some converge and some are divergent. The molecular properties of some of the well-characterised representatives of two-component systems comply with the requirements to be put upon the elements of a neural network: they function as logical operators and show the phenomenon of autoamplification. Because there are many phosphoryl transfer pathways in parallel and because there also appears to be cross-talk between these pathways, the total of all two-component regulatory systems in a single prokaryotic cell may show the typical characteristics of a 'phospho-neural network'. This may well lead to signal amplification, associative responses and memory effects, characteristics which are typical for neural networks. One of the main challenges in molecular microbial physiology is to determine the extent of the connectivity of the constituting elements of this presumed 'phospho-neural network', and to outline the extent of intelligence-like behaviour this network can generate. Escherichia coli is the organism of choice for this characterization.