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Elasmobranch species in the North-East Atlantic have rarely been assessed over the past decades. A European research project (DELASS) has been initiated in 2000 to remedy this deficiency. A number of case study species were chosen from the rays, the coastal sharks, the deepwater sharks and the pelagic sharks. With the available data that could be collected from the partners in the project stock assessment models of very different scope and complexity have been applied. Initial results of the assessments are summarized in the paper. Implications for further research and for the management of elasmobranch species are discussed