The response properties and directional receptive fields of nonspiking local interneurons in the cercal system of the cockroach are described. Wind-evoked responses were recorded intracellularly, and then analyzed by means of the Wiener kernel method in which a Gaussian white noise signal was used as a stimulus. Cross-correlation between the response and the white noise signal produced first- (linear) and second-order (nonlinear) kernels that were used to define input-output characteristics of the interneurons. Three sets of interneurons were distinguished on the basis of kernel analysis. First, responses in interneurons 101, 107, 111, and 203 were characterized predominantly by a differentiating first-order kernel, which suggests a linear relationship to the stimulus. The amplitude and waveform of the kernel changed with the change in stimulus angle, indicating that these four cells are directionally sensitive. Second, responses in interneurons 102 and 103 were also directionally sensitive but highly nonlinear. The first-order kernel was biphasic, whereas the second-order kernel had an elongated depolarizing peak on the diagonal. The response dynamics were accounted for by a cascade of two filters, a linear band-pass filter and a static nonlinear filter, in which the nonlinearity is a signal compression (or a rectification). Third, responses in interneurons 104 and 201 consist largely of the second-order nonlinear component. The second-order kernel, which had an elongated depolarizing peak or a hyperpolarizing valley on the diagonal, did not show any directional preference. The second-order nonlinearity was dynamic, and could be modeled by a band-pass linear filter-static nonlinearity-low-pass linear filter cascade, where the static nonlinearity is a full-wave rectification. The band-pass filter would simply reflect the mechanical property of cercal hair sensilla, whereas the low-pass filter represents the transfer at synapses between the cercal afferents and the interneurons. The nonlinear response thus explains the difference in the directional sensitivity while the differentiating first-order kernel explains the velocity sensitivity of the interneurons. We show that 101 and 107 respond most preferentially to wind from the left versus right, whereas 102, 103, 111, and 203 respond to wind from the front versus rear. Thus, it is suggested that there are two subsystems responding maximally to wind displacement along two coordinate directions, one for the longitudinal direction and the other for the transverse direction. On the other hand, the full-wave-rectifier nonlinear interneurons are omnidirectional, and thus suggested to code simply the power of the wind displacement.