Originally considered as a local development problem, combating desertification is viewed more and more as a global environmental issue at the international level. May combating desertification be considered a global public good? The document shortly describes the desertification problem, its extent and examples of available solutions for stopping it. However, the analysis of the links between desertification and social changes - particularly the ones that relate to migration, poverty and land tenure -, demonstrates the interest of broadening the traditional approach of combating desertification. Such a focus highlights the need for implementing a consistent set of interdependent actions to solve desertification problems. These actions should be designed in each situation at various levels, from local to global, and supported by as many specific institutional arrangements. The discussion brings into debate elements for deciding whether combating desertification should or should not be recognized as being a global public good and for identifying which new fighting mechanisms should be implemented at international levels.