The brainstem circuitry underlying saccades is symmetrical with respect to the midline. The oculomotor behaviour generated by the circuitry depends on a combination of signals passed along fibre tracts and less easily identifiable connections, such as those across the midline. The midline crossing connections are often affected by developmental disorders which give rise to unstable eye movements (see J. Jen, this volume). The connections at the levels of the colliculus, pause cells, and neural integrator generate different dynamical mechanisms for the development of instabilities, which can be identified in eye movement recordings using phase space analysis techniques.