The event-driven nature of spiking neural networks makes them biologically plausible and more energy-efficient than artificial neural networks. In this work, we demonstrate motion detection of an object in a two-dimensional visual field. The network architecture presented here is biologically plausible and uses CMOS analog leaky integrate-and-fire neurons and ultra-low power multi-layer RRAM synapses. Detailed transistorlevel SPICE simulations show that the proposed structure can accurately and reliably detect complex motions of an object in a two-dimensional visual field.