This paper describes a systematic approach to predict ash deposits in coal-fired boilers by means of artificial neural networks. The approach is of a "grey box" nature, decomposing the problem into logical parts, and avoiding the use of sophisticated data. Although it is relative to the specific fuel and equipment, the prediction is very detailed and can be used on-line; it accounts not only for the deposition rate, but also for short-term cleaning occurrences, thus simulating a complex and chaotic time-evolution. The model is developed with the aid of a case-study, that of the fouling of a furnace, as detected by heat flux meters. Provided that an adequate amount of heat transfer measurements can be gathered, the procedure can be used to simulate the evolution of boiler heat absorption under realistic conditions of deposition. Applications include obviously new possibilities for automatic control of the equipment, as well as the optimization of operating set points to maximize thermal efficiency, such as the sequence and operation of on-load cleaning devices. It is thought that the method developed would be applicable to other instances of fouling or equipment degradation exhibiting similar behavior, specially with respect to on-line corrective measures. (c) 2005 Elsevier Ltd. All rights reserved.