The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in convective heated surfaces of boilers, namely superheaters and economizers. The proposed model is based on solving equation describing the energy conservation and is simplified because the mass and momentum balance equations are omitted. The suggested method considers the superheater or economizer model as one with distributed parameters. The temperature of the separating wall is determined from the equation of transient heat conduction. In order to obtain a grater accuracy of the results, the wall was divided into two control volumes making it possible to compute the temperatures on its both surfaces. All thermo-physical properties of the operating media and the material of the separating walls are computed in real time. The space-time heat transfer coefficients are also computed on-line considering the actual tube pitches and assuming cross-flow of the combustion gases. In the proposed model the boundary conditions can be time-dependent. In order to experimentally verify the proposed method for modelling the processes occurring in convective surfaces of power boilers, a series of measurements of the platen superheater and economizer in an OP-210 boiler (with steam capacity of 210×103 kg/h) were carried out. Comparing the results of measurements of the steam and feed water temperature with computation results, satisfactory convergence is found.