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Viral liver infections with parenteral transmission in Western countries are mostly caused by hepatitis B and hepatitis C viruses (HBV and HCV). This paper presents a mathematical model that describes the history of the spread of HBV and HCV infections in the general population in Italy. The analysis of the model and the results also provide some new insight into the mechanisms of the epidemics. The model structure is based on an underlying analysis of the various effects of the infection progression in the host, in order to incorporate into its parameters most of the information available from the literature. Moreover, incidence and prevalence curves of both HBV and HCV infections and of HBV/HCV co-infections are generated and qualitative aspects of the epidemic, such as possible endemic steady states and the basic reproduction number, are also analyzed.