For many animals, target motion carries high ecological significance as this may be generated by a predator, prey, or potential mate. Indeed, animals whose survival depends on early target detection are often equipped with a sharply tuned visual system, yielding robust performance in challenging conditions. For example, many fast-flying insects use visual cues for identifying targets, such as prey (e.g., predatory dragonflies and robberflies) or conspecifics (e.g., nonpredatory hoverflies), and can often do so against self-generated background optic flow. Supporting these behaviors, the optic lobes of insects that pursue targets harbor neurons that respond robustly to the motion of small moving objects, even when displayed against syn-directional background clutter. However, in diptera, the encoding of target information by the descending neurons, which are more directly involved in generating the behavioral output, has received less attention. We characterized target-selective neurons by recording in the ventral nerve cord of male and female predatory Holcocephala fusca robberflies and of male nonpredatory Eristalis tenax hoverflies. We show that both species have dipteran target-selective descending neurons that only respond to target motion if the background is stationary or moving slowly, moves in the opposite direction, or has un-naturalistic spatial characteristics. The response to the target is suppressed when background and target move at similar velocities, which is strikingly different to the response of target neurons in the optic lobes. As the neurons we recorded from are premotor, our findings affect our interpretation of the neurophysiology underlying target-tracking behaviors.