Observations and analysis of medical anthropologists have stressed on the complex interactions between conventional and unconventional medicines in chronic diseases. The dominant position of the biomedicine is shaping the practices' legitimacy according to political, medical and scientific agendas in each country. The notion of Complementary and Alternative Medicines (CAM) recently used in the medical sphere shows a new trend in the biomedical system to open it to complementary approaches. But the notion of CAM brings a binary system centred on the biomedical paradigm in identifying the acceptable approaches to complement conventional treatment and the non-acceptable one as alternative to official ones. We propose here to consider the margins of the biomedical system as a floating sphere where the two types of approaches exist together. It is proposed to bring first-hand field illustrations and proposals of new analysis to these complex relationships between conventional and unconventional cure and care of chronic diseases bringing an anthropological and theorical framework. Here are below some preliminary questions: What are revealing these margins for the biomedical system and for the unconventional practices? Are they acting to change (deeply?) the biomedical system? Are the unconventional practices getting a better recognition to be used in biomedical institutions? What are bringing the double perspectives of conventional and unconventional practiced by medical doctors for the medical system and for the cure of the patients? Is there any common (and non only complementary) therapeutic space where borders between biomedicine and CAMs get confused (reorganization, acculturation, crisis, synthesis, syncretism, etc.)?