A "temporal gradient apparatus" has been developed that allows the motility of bacteria to be studied after they have been subjected to a sudden change from one uniform concentration of attractant to another. A sudden decrease elicits the tumbling response observed with spatial gradients; it was found, however, that a sudden increase also elicits a response, namely supercoordinated swimming. This demonstrates that chemotaxis is achieved by modulation of the incidence of tumbling both above and below its steady-state value. The initial responses gradually revert to the steady-state motility pattern characteristic of a uniform distribution of attractant. The apparent detection of a spatial gradient by the bacteria therefore involves an actual detection of a temporal gradient experienced as a result of movement through space. Potential models for the chemotactic response based on some "memory" mechanism are discussed.