Information processing in neural networks by computation with attractors (steady states, limit cycles, strange attractors) has been extensively discussed in application to many neural systems: central pattern generators, sensory systems (e.g. visual, olfactory), hippocampus, etc. Computation with attractors in a traditional way faces а fundamental contradiction between robustness and sensitivity. In this paper we discuss а new direction in information neurodynamics based on experiments performed in the locust olfactory system, the orientation sensory system of the marine mollusk Clione апа the hippocampal place cell networks. This new concept uses the transformation of the incoming spatial or identity information into spatio-temporal output based on the intrinsic switching dynamics of neural networks with nonsymmetric inhibitory connections. This is called the Winner-Less Competition Principle (WLC). The key feature of а network that computes with separatrices is the robustness against noise and the simultancous sensitivity of the sequence of switching to the incoming information. We present rigorous results about the stability of the sequential switching in the framework оf the Lottka-Volterra model. Because оf their fast reaction, the discussed neural networks are able 10 change their intrinsic dynamics to respond to new incoming information and solve many different functional tasks. Computation with separatrices can also be an optimal principle for the design of new paradigms of artificial neural networks.