The article deals with a the ethical issues about treatment of Persistent Vegetative State (Pvs) patients. The Nancy Beth Cruzan case, the US woman who died after the withdrawal of tube feeding and hydration after seven years of Pvs is analysed as paradigmatic case. The ethical analysis face with the following issues: 1. Is the Pvs synonymous of cerebral death?; 2. How the tube feeding and hydration must be considered: ordinary or extraordinary, proportionate or disproportionate means? 3. The issue of the living will; 4. the economic impact of the management of the Pvs patients. The conclusion of the contribution is the following: the withdrawal of the artificial feeding and hydration of a Pvs patient must be considered as omissive euthanasia, and consequently it is an action ethically unacceptable, in the light of the Hippocratic medical tradition and of the person-centred ethics.