"Imagine a tenth of a mile of river front with an unbroken line of trees with fireflies on ever leaf flashing in synchronism. ... Then, if one's imagination is sufficiently vivid, he may form some conception of this amazing spectacle." So wrote the naturalist Hugh Smith. In this article we consider how one might model mathematically the synchronization between two fireflies using a system of differential equations that represent two coupled biological clocks with sine and square-wave interactions.