A new methodology has been developed for the assessment of the annual effective dose resulting from removable and fixed radiological surface contamination. It is entitled SUDOQU (SUrface DOse QUantification) and it can for instance be used to derive criteria for surface contamination related to the import of non-food consumer goods, containers and conveyances, e.g., limiting values and operational screening levels. SUDOQU imposes mass (activity)-balance equations based on radioactive decay, removal and deposition processes in indoor and outdoor environments. This leads to time-dependent contamination levels that may be of particular importance in exposure scenarios dealing with one or a few contaminated items only (usually public exposure scenarios, therefore referred to as the 'consumer' model). Exposure scenarios with a continuous flow of freshly contaminated goods also fall within the scope of the methodology (typically occupational exposure scenarios, thus referred to as the 'worker model'). In this paper we describe SUDOQU, its applications, and its current limitations. First, we delineate the contamination issue, present the assumptions and explain the concepts. We describe the relevant removal, transfer, and deposition processes, and derive equations for the time evolution of the radiological surface-, air- and skin-contamination levels. These are then input for the subsequent evaluation of the annual effective dose with possible contributions from external gamma radiation, inhalation, secondary ingestion (indirect, from hand to mouth), skin contamination, direct ingestion and skin-contact exposure. The limiting effective surface dose is introduced for issues involving the conservatism of dose calculations. SUDOQU can be used by radiation-protection scientists/experts and policy makers in the field of e.g. emergency preparedness, trade and transport, exemption and clearance, waste management, and nuclear facilities. Several practical examples are worked out demonstrating the potential applications of the methodology.