Information on the transient response of heat exchangers is essential to produce the optimum heat exchanger operation for the required function. A transient response analysis is presented for a heat exchanger with an infinite capacitance fluid on the shell side. The inlet temperature of the finite capacity fluid is stepped, and the heat exchanger response is represented by the change in the temperature of this fluid at the outlet of the tubes. The results cover all practical combinations of the dependent parameters and are presented as a set of charts. Results of previous workers in this field are discussed. Their charts cover a very restricted range of heat transfer conditions and are therefore of limited use. In addition, assumptions have been incorporated into their analyses which result in major discrepancies.