The next generation of High Energy Physics experiments requires a GRID approach to a distributed computing system and the associated data management: the key concept is the Virtual Organisation (VO), a group of geographycally distributed users with a common goal and the will to share their resources. A similar approach is being applied to a group of Hospitals which joined the GPCALMA project (Grid Platform for Computer Assisted Library for MAmmography), which will allow common screening programs for early diagnosis of breast and, in the future, lung cancer. HEP techniques come into play in writing the application code, which makes use of neural networks for the image analysis and shows performances similar to radiologists in the diagnosis. GRID technologies will allow remote image analysis and interactive online diagnosis, with a relevant reduction of the delays presently associated to screening programs.