The dynamic behaviour of one-dimensional flow (cocurrent and countercurrent) multistream heat exchangers and their networks is modelled and simulated. The problems can be classified into two types: (1) dynamic responses to arbitrary temperature transients and to sudden flow rate transients from a uniform temperature initial condition or a steady-state condition, which yield a linear mathematical model; (2) dynamic responses to disturbances in thermal flow rates, heat transfer coefficients or flow distributions, which are non-linear problems and should be solved numerically. A linearized model is developed to solve the non-linear problems with small disturbances. The linear model and the linearized model for small disturbances are solved by means of Laplace transform and numerical inverse algorithm. Introducing four matching matrices, the general solution can be applied to various types of one-dimensional flow multistream heat exchangers such as shell-and-tube heat exchangers and plate heat exchangers as well as their networks. The time delays in connecting and bypass pipes are included in the models. The software TAIHE (transient analysis in heat exchangers) is further developed to include the present general solution and is applied to the simulation of fluid temperature responses of multistream heat exchangers. Examples are given to illustrate the procedures in detail.