1 Cockroaches (Periplaneta americana) that were restrained but were able to make normal walking movements were stimulated with wind puffs delivered to the cereal wind receptors. Some puffs were superimposed on a constant ‘headwind’ simulating the relative wind that the walking cockroach would experience if it were not fixed in place. Puffs were either of variable peak velocity, or of fixed peak velocity but variable acceleration. In some experiments the movement responses of one metathoracic leg were recorded; in other experiments the responses of giant interneurons were recorded. 2. The threshold wind velocity of 3 mm/s for evoking a behavioral response in slowly walking cockroaches (Camhi and Nolen 1981) was still effective even in the presence of an 80 mm/s headwind. Measurements of the background wind (‘noise’) near a cercus of a slowly walking cockroach in the headwind showed a mean velocity of about 80 mm/s plus periodic wind gusts of up to 30 mm/s produced by the stepping motions of the legs (Fig. 3). Although over 50% of these gusts have velocities greater than the threshold stimulus for evoking a behavior (Fig. 4A), the cockroach did not respond to these gusts. However, the maximal accelerations of these gusts were consistently less than that of the just-threshold wind puff (Fig. 4B). 3. Stimuli of high acceleration (greater than 600 mm/s2) usually evoked running. Those of intermediate acceleration (approximately 300 mm/s2) usually evoked a pause in walking. The lower the acceleration, the greater the incidence of no response (Fig. 7A). This discrimination of wind acceleration was generally the same even when the stimuli were superimposed on the headwind (Fig. 7B). The discrimination of acceleration was also independent of the direction of the wind stimuli (Fig. 7C, D). 4. The wind made by the strike of a natural predator, the toadBufo marinus (known to be the cue by which cockroaches detect and respond to the toad; Camhi et al. 1978) produces a sufficiently high wind acceleration, sufficiently early, to account for the cockroach's running response to the wind made by the strike. 5. In electrical recordings from a single connective of the ventral nerve cord, it was possible to identify the action potentials from the group of three largest giant interneurons, No.'s 1, 2, and 3, which may mediate the initiation of escape behavior (Camhi and Nolen 1981). The number and frequency of action potentials in these neurons were greater for wind stimuli of higher acceleration, even though the peak wind velocity of all stimuli was the same (Fig. 10). 6. The results indicate that wind acceleration is a crucial cue by which the cockroach escape system discriminates wind signals, including the wind from the strike of a predator, from background noise, including that produced by the animal's own walking.