Fundamental equations of a multi-concentric cylindrical heat exchanger that can treat flow rate change are obtained. Matrix transfer functions of the outlet temperature change to the flow rate change are gained and the theoretical frequency responses for the four types of heat exchanger are calculated to show the influence of the heat transfer through the baffle cylinders. Numerical results of the four types are analyzed and compared form the viewpoint of control and it is shown that a counter-flow type has the best dynamic characteristics. Furthermore, it is suggested thet the dynamic characteristics of the multi-concentric cylindrical heat exchanger can be approximated by another heat exchanger called the cone type heat exchanger of the second order, and the fundamental equations of the cone type heat exchanger are obtained.