<p>An investigation has been made into the limits of the heat exchange process at limitations placed on the heat load and the heat-transfer coefficient, for a constant heat capacity of flows and for a heat capacity depending on temperature. In particular, such dependence occurs for flows changing their phase state. It is shown that the replacement of variables in a mathematical model of a process makes it possible to obtain solutions retaining its form at any kinetics. The notion of thermodynamically equivalent heat-exchange systems has been introduced, which has made it possible to reduce the synthesis of a multi-flow heat-exchange system to solving two ordinary differential equations with separable variables describing a two-flow heat exchange between flows with variable heat capacity is suggested. Based on the obtained results, an algorithm for synthesis of multi-flow heat-exchange systems is suggested. In the system being synthesized, each flow can contact several flows, limitations on temperatures, flow rates and heat capacities of all or part of flows dictated by the technological process integrated with the system are fulfilled. The system′s synthesis implies the selection of a structure of contacts, values of free parameters of the flows, a distribution of contact surfaces and heat loads between two-flow heat exchange cells.</p>