Responses of tethered cells of Escherichia coli to impulse, step, exponential-ramp or exponentiated sine-wave stimuli are internally consistent, provided that allowance is made for the nonlinear effect of thresholds. This result confirms that wild-type cells exposed to stimuli in the physiological range make short-term temporal comparisons extending 4 sec into the past: the past second is given a positive weighting, the previous 3 sec are given a negative weighting, and the cells respond to the difference. cheRcheB mutants (defective in methylation and demethylation) weight the past second in a manner similar to the wild type, but they do not make short-term temporal comparisons. When exposed to small steps delivered iontophoretically, they fail to adapt over periods of up to 12 sec; when exposed to longer steps in a flow cell, they partially adapt, but with a decay time of greater than 30 sec. cheZ mutants use a weighting that extends at least 40 sec into the past. The gain of the chemotactic system is large: the change in occupancy of one receptor molecule produces a significant response.