The information processing capabilities of biomolecular excitable media based on nonlinear dynamic mechanisms are discussed. Given even the simplest medium geometry, dynamics and information processing features inherent in biomolecular excitable media proves to be diverse and sophisticated. For the case of pseudo two-dimensional versions these media can be described in terms of neural networks having lateral connections. The main responses of shunting on-center off-surround feedback neural networks and pseudo two-dimensional excitable systems to the external excitations are surprisingly similar. The excitable media are capable of short-time memory, of contour enhancement and quenching or amplifying small features depending on medium state. The analogies discussed reaffirm specific neural net characteristics of excitable media and give the opportunity to estimate more accurate excitable medium characteristics.