Abstract The paper presents a discussion of parameterized discrete dynamics of neural ring networks. For specific parameter domains stable periodic orbits coexist. Their periods and the number of orbits of a given period are determined. Even n-rings (i.e., rings with an even number of inhibitory connections) exhibit mainly stable period-n orbits. Odd n-rings display mainly stable period-2n orbits. The dynamical effects of inhibitory connections are analysed, and a characterization of attractors in terms of their “firing pattern” is presented.