Oil spills represent a major threat to ocean ecosystems and their health. Illicit pollution requires continuous monitoring and satellite remote sensing technology represents an attractive option for operational oil spill detection. Previous studies have shown that active microwave satellite sensors, particularly Synthetic Aperture Radar (SAR) can be effectively used for the detection and classification of oil spills. Oil spills appear as dark spots in SAR images. However, similar dark spots may arise from a range of unrelated meteorological and oceanographic phenomena, resulting in misidentification. A major focus of research in this area is the development of algorithms to distinguish oil spills from `look-alikes'. This paper describes the development of a new approach to SAR oil spill detection employing two different Artificial Neural Networks (ANN), used in sequence. The first ANN segments a SAR image to identify pixels belonging to candidate oil spill features. A set of statistical feature parameters are then extracted and used to drive a second ANN which classifies objects into oil spills or look-alikes. The proposed algorithm was trained using 97 ERS-2 SAR and ENVSAT ASAR images of individual verified oil spills or/and look-alikes. The algorithm was validated using a large dataset comprising full-swath images and correctly identified 91.6% of reported oil spills and 98.3% of look-alike phenomena. The segmentation stage of the new technique outperformed the established edge detection and adaptive thresholding approaches. An analysis of feature descriptors highlighted the importance of image gradient information in the classification stage.