The question of how deep ocean eddies can cross the equator is addressed with the aid of analytical and numerical models. We focus on the possibility that deep ocean (lens-like) eddies can cross the equator via deep cross equatorial channels on the ocean floor. We first examine the behavior of solid balls (i.e., free particles) in a meridional parabolic channel on a β plane. Such balls are subject to similar topographical forcing and inertial forces that a lens is subject to, except that pressure forces and friction are absent. We examine both single isolated balls and a “cloud” of (noninteractive) balls. In general, the balls' trajectories have a chaotic character; a fraction of the cloud crosses the equator and ends up in the northern hemisphere, and a fraction is left behind. More realistic numerical experiments (with a fully nonlinear reduced-gravity isopycnic model of the Bleck and Boudra type) show similar behavior. In all cases the equator acts as an “eddy smasher” in the sense that it breaks the lens into at least two parts, one crosses the equator and ends up in the northern hemisphere, and the other is left behind. Here, however, the system is not chaotic. Despite the obvious differences between clouds of balls and eddies, there is a remarkable similarity between the percentage of balls that penetrate into the opposite hemisphere and the percentage of eddies' mass that ends up in the other hemisphere. This suggests that the geometry of the channel and the presence of the equator determine how the fluid will be partitioned among the two hemispheres.