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Regions of Restricted Exchange (RREs) are an important feature of the European coastline. They are historically preferred sites for human settlement and aquaculture and their ecosystems, and consequent human use, may be at risk from eutrophication. The OAERRE project (EVK3-CT1999-0002) concerns 'Oceanographic Applications to Eutrophication in Regions of Restricted Exchange'. It began in July 2000, and studies six sites. Four of these sites are fjords: Kongsfjorden (west coast of Spitzbergen); Gullmaren (Skagerrak coast of Sweden); Himmerfjarden (Baltic coast of Sweden); and the Firth of Clyde (west coast of Scotland). Two are bays sheltered by sand bars: Golfe de Fos (French Mediterranean); and Ria Formosa (Portuguese Algarve). Together they exemplify a range of hydrographic and enrichment conditions. The project aims to understand the physical, biogeochemical and biological processes, and their interactions, that determine the trophic status of these coastal marine RRE through the development of simple screening models to define, predict and assess eutrophication. This paper introduces the sites and describes the component parts of a basic screening model and its application to each site using historical data. The model forms the starting point for the OAERRE project and views an RRE as a well-mixed box, exchanging with the sea at a daily rate E determined by physical processes, and converting nutrient to phytoplankton chlorophyll at a fixed yield q. It thus uses nutrient levels to estimate maximum biomass; these preliminary results are discussed in relation to objective criteria used to assess trophic status. The influence of factors such as grazing and vertical mixing on key parameters in the screening model are further studied using simulations of a complex 'research' model for the Firth of Clyde. The future development of screening models in general and within OAERRE in particular is discussed. In addition, the paper looks ahead with a broad discussion of progress in the scientific understanding of eutrophication and the legal and socioeconomic issues that need to be taken into account in managing the trophic status of RREs.