Screening programmes for diabetic retinopathy are being introduced in the United Kingdom and elsewhere. These require large numbers of retinal images to be manually graded for the presence of disease. Automation of image grading would have a number of benefits. However, an important prerequisite for automation is the accurate location of the main anatomical features in the image, notably the optic disc and the fovea. The locations of these features are necessary so that lesion significance, image field of view and image clarity can be assessed. This paper describes methods for the robust location of the optic disc and fovea. The elliptical form of the major retinal blood vessels is used to obtain approximate locations, which are refined based on the circular edge of the optic disc and the local darkening at the fovea. The methods have been tested on 1056 sequential images from a retinal screening programme. Positional accuracy was better than 0.5 of a disc diameter in 98.4% of cases for optic disc location, and in 96.5% of cases for fovea location. The methods are sufficiently accurate to form an important and effective component of an automated image grading system for diabetic retinopathy screening.