The discrete dynamics of a dissipative nonlinear model neuron with self-interaction is discussed. For units with self-excitatory connection hysteresis effects, i.e. bistability over certain parameter domains, are observed. Numerical simulations demonstrate that self-inhibitory units with non-zero decay rates exhibit complex dynamics including period doubling routes to chaos. These units may be used as basic elements for networks with higherorder information processing capabilities. appeared in: Physica D, 104, 205 - 211, 1997. 1 1 Introduction Biological neurons exhibit a large variety of dynamical behaviors even when they are not embedded in a network. This type of dynamics is captured by biologically inspired neuron models like the Hodgkin-Huxley  or the FitzHugh-Nagumo equations , . On the other hand, formal neurons used in artificial neural networks like the McCulloch-Pitts neuron or the graded response neurons  have only trivial, i.e. convergent dynamics as s..