An approach to information processing based on the excitation of patterns of activity by non-linear active resonators in response to their input patterns is proposed. Arguments are presented to show that any computation performed by a conventional Turing machine-based computer, called T-machine in this paper, could also be performed by the pattern excitation-based machine, which will be called P-machine. A realization of this processing scheme by neural networks is discussed. In this realization, the role of the resonators is played by neural pattern excitation networks, which are the neural circuits capable of exciting different spatio-temporal patterns of activity in response to different inputs. Learning in the neural pattern excitation networks is also considered. It is shown that there is a duality between pattern excitation and pattern recognition neural networks, which allows to create new pattern excitation modes corresponding to recognizable input patterns, based on Hebbian learning rules. Hierarchically organized, such networks can produce complex behavior. Animal behavior, human language and thought are treated as examples produced by such networks.