Complete elimination of fouling in heat transfer equipment is rarely achieved in practice, so cleaning of fouled units is a regular task in the process industries. Algorithms for scheduling cleaning have, to date, minimized the net losses due to fouling by focusing on when and which units to clean. In contrast, this paper focuses on when and how to clean a unit, when more than one cleaning method is available. The model formulation is approached by idealizing a foulant deposit as consisting of two layers, soft (fresh) and hard(aged). The hard material is formed through the ageing of the soft material. Hard deposits are more difficult to remove and require time- and cost-intensive cleaning methods (such as mechanical cleaning). Soft deposits are removed through less time- and cost-intensive methods such as chemical cleaning by recirculation of solvents. The hard deposit usually consists of more thermally conductive material and hence, for a given thickness, has a lower thermal resistance compared to the soft deposit. This work introduces a new methodology to identify optimum cleaning cycles (OCCs) under the presence of both soft and hard deposit, when two cleaning methods (solvent and mechanical cleaning) are available. The analysis of OCCs is extended and a new concept called the 'cleaning supercycle' is elaborated, which can be related to the optimal time between plant shutdowns. (c) 2010 Elsevier Ltd. All rights reserved.