The understanding of the overall dynamics of the Mediterranean realm represents a major concern for its populations, as well as for other nations who are depending on its energy, mineral and other natural resources, as well as its manpower and economy. Preservation of the environment and assessment of natural risks (such as seismic hazards) and anthropic risks are two important concerns that must be kept in mind when exploiting Mediterranean resources. Dealing with these concerns would require a good understanding of the many parameters controlling resource distribution and the genesis of natural hazards and risks. Therefore, the Mediterranean system as a whole needs to be better understood, from the dynamics of the lithosphere and underlying mantle up to its interactions with the climate and anthropic activities. The TerMEx project will address two sets of major challenges, i.e. societal challenges associated with natural hazards, resources and climate change), as well as scientific challenges such as the deep Earth dynamics, its interactions with climate, and the overall evolution of the Mediterranean ecosystems. Research projects of the TerMEx programme will be undertaken in the framework of a circum-Mediterranean cooperation.