Ephaptic coupling refers to interactions between neurons mediated by current flow through the extracellular space. Ephaptic interactions between axons are considered negligible, because of the relatively large extracellular space and the layers of myelin that separate most axons. By contrast, olfactory nerve axons are unmyelinated and arranged in tightly packed bundles, features that may enhance ephaptic coupling. We tested the hypothesis that ephaptic interactions occur in the mammalian olfactory nerve with the use of a computational approach. Numerical solutions of models of axon fascicles show that significant ephaptic interactions occur for a range of physiologically relevant parameters. An action potential in a single axon can evoke action potentials in all other axons in the fascicle. Ephaptic interactions can also lead to synchronized firing of independently stimulated axons. Our findings suggest that ephaptic interactions may be significant determinants of the olfactory code and that such interactions may occur in other, similarly organized axonal or dendritic bundles.