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Population dynamics of multiple interactive species in rivers and streams is important in river/stream ecology. In this paper, we consider a model for two competitive species living in a river environment where the populations grow and compete in the benthic zone and disperse in the drifting water zone. We establish threshold conditions for persistence and extinction of two species and obtain the existence of a positive steady state under persistence conditions. We also numerically investigate the influences of factors, such as advection rates, diffusion rates, river length, competition rates, transfer rates, and spatial heterogeneity on persistence of the two competitive species.