The subject of this paper is the steam boiler nonlinear mathematical model. The furnace chamber heat transfer is modelled assuming that the flue gas temperature across the entire furnace chamber is constant. Only radiation heat transfer to the boiler waterwalls is modelled. Distributed parameter mathematical models are developed of the steam superheater individual stages: the superheater first stage, the platen superheater, the second and third stage of the superheater. In the same way, the boiler two-stage economizer is modelled. The flue gas and air temperatures downstream the air heater individual stages are determined using the epsilon-NTU method (effectiveness epsilon - the number of transfer units NTU). Due to such arrangement of the boiler heating surfaces and the heat transfer nonlinear character, iterative calculations of the steam, flue gas, and air temperatures are necessary. The developed mathematical model makes it also possible to determine temperatures of the tube outer and inner surfaces and external fouling for all heating surfaces of the boiler. The developed non-linear mathematical model of the entire boiler has high practical importance. The proposed mathematical model can be used to simulate the boiler operation in various conditions, allowing to determine and correct selection the parameters of boiler operation. A non-linear mathematical model of the boiler can also be used to design the individual stages of the superheater properly so as to achieve the desired temperature behind the individual stages. Determination of the local temperature of the tube wall allows selecting an appropriate grade of steel for the individual stages of the superheater. Also, the developed non-linear mathematical model can be used for boiler operation monitoring in on-line mode. (C) 2019 Elsevier Ltd. All rights reserved.