Determination of the dynamical structure of neural circuits--the general principles of how neural activity varies with time and manipulates information--is a prerequisite to understanding their computational function. Rhythmically active or oscillating neural circuits are particularly interesting dynamical structures, as rhythms and oscillations are a prominent feature of mammalian central nervous system electrophysiology. Coherent oscillations by networks of interneurons are observed in the vertebrate olfactory system and have recently been described in mammalian visual cortex. These interneuronal networks display oscillations in local field potential (LFP) and probability of producing action potentials that are highly correlated between subcircuits sharing the same stimulus features. Much less is known about the existence and importance of network oscillations in the higher centres of invertebrates. Here we report that a network of olfactory interneurons in the cerebral ganglion of the terrestrial mollusc Limax maximus also displays coherent oscillations in LFP which are modified by odour input. This dynamical structure could be central to the odour recognition and odour learning ability of Limax.