In this paper we study disease transmission with two distinct strains from the same pathogen on scale-free networks with saturated infection rates.By using a mean-field method, we build two-strain epidemic models according to both a perfect cross-immunity mechanism and a super-infection mechanism.The epidemic dynamics on complex networks is generally determined by network structure, infectious mechanism: and interaction manner between strains.We examine strain coexistence, strain replacement, and strain dominance, and show good agreement between theory and numerical simulations.We find that different interaction mechanisms can lead to different effects.