Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.