Abstract. The tangential neurons in the lobula plate region of the flies are known to respond to visual motion across broad receptive fields in visual space. When intracellular recordings are made from t angential neurons while the intact animal is stimulated visually with moving natural imagery, we find that neural response depends upon speed of motion but is nearly invariant with respect to variations in natural scenery. We refer to this invariance as velocity constancy. It is remarkable because natural scenes, in spite of similarities in spatial structure, vary considerably in contrast, and contrast dependence is a feature of neurons in the early visual pathway as well as of most models for the elementary operations of visual motion detection. Thus, we expect that operations must be present in the processing pathway that reduce contrast dependence in order to approximate velocity constancy. We consider models for such operations, including spatial filtering, motion adaptation, saturating nonlinearities, and nonlinear spatial integration by the tangential neurons themselves, and evaluate their effects in simulations of a tangential neuron and precursor processing in response to animated natural imagery. We conclude that all such features reduce interscene variance in response, but that the model system does not approach velocity constancy as closely as the biological tangential cell.