The empirical literature on the measurement of health inequalities is vast and rapidly expanding. To date, however, no foundation in welfare economics exists for the proposed measures of health inequality. This paper provides such a foundation for commonly used measures like the health concentration index, the Gini index, and the extended concentration index. Our results indicate that these measures require assumptions that appear restrictive. One way forward may be the development of multi-dimensional extensions. (c) 2006 Elsevier B.V. All rights reserved.