In animal species ranging from invertebrate to mammals, visually guided escape behaviours have been studied using looming stimuli, the two-dimensional expanding projection on a screen of an object approaching on a collision course at constant speed. The peak firing rate or membrane potential of neurons responding to looming stimuli often tracks a fixed threshold angular size of the approaching stimulus that contributes to the triggering of escape behaviours. To study whether this result holds more generally, we designed stimuli that simulate acceleration or deceleration over the course of object approach on a collision course. Under these conditions, we found that the angular threshold conveyed by collision detecting neurons in grasshoppers was sensitive to acceleration whereas the triggering of escape behaviours was less so. In contrast, neurons in goldfish identified through the characteristic features of the escape behaviours they trigger, showed little sensitivity to acceleration. This closely mirrored a broader lack of sensitivity to acceleration of the goldfish escape behaviour. Thus, although the sensory coding of simulated colliding stimuli with non-zero acceleration probably differs in grasshoppers and goldfish, the triggering of escape behaviours converges towards similar characteristics. Approaching stimuli with non-zero acceleration may help refine our understanding of neural computations underlying escape behaviours in a broad range of animal species. KEY POINTS: A companion manuscript showed that two mathematical models of collision-detecting neurons in grasshoppers and goldfish make distinct predictions for the timing of their responses to simulated objects approaching on a collision course with non-zero acceleration. Testing these experimental predictions showed that grasshopper neurons are sensitive to acceleration while goldfish neurons are not, in agreement with the distinct models proposed previously in these species using constant velocity approaches. Grasshopper and goldfish escape behaviours occurred after the stimulus reached a fixed angular size insensitive to acceleration, suggesting further downstream processing in grasshopper motor circuits to match what was observed in goldfish. Thus, in spite of different sensory processing in the two species, escape behaviours converge towards similar solutions. The use of object acceleration during approach on a collision course may help better understand the neural computations implemented for collision avoidance in a broad range of species.