In this paper, a PDE-based system for detecting the boundary of skin lesions in digital clinical skin images is presented. The image is first-processed via contrast-enhancement and anisotropic diffusion. If the lesion is covered by hairs, a PDE-based continuous morphological filter that removes them is used as an additional pre-processing step. Following these steps, the skin lesion is segmented either by the geodesic active contours model or the geodesic edge tracing approach. These techniques are based on computing, again via PDE's, a geodesic curve in a space defined by the image content. Examples showing the performance of the algorithm are given.