As the number of biological invasions increases, interactions between different invasive species will become increasingly important. Several studies have examined facilitative invaderinvader interactions, potentially leading to invasional meltdown. However, if invader interactions are negative, invasional interference may lead to lower invader abundance and spread. To explore this possibility, we develop models of two competing invaders. A landscape simulation model examines the patterns created by two such species invading into the same region. We then apply the model to a case study of Carduus nutans L. and C. acanthoides L., two economically important invasive weeds that exhibit a spatially segregated distribution in central Pennsylvania, USA. The results of these spatially-explicit models are generally consistent with the results of classic LotkaVolterra competition models, with widespread coexistence predicted if interspecific effects are weaker than intraspecific effects for both species. However, spatial segregation of the two species (with lower net densities and no further spread) may arise, particularly when interspecific competition is stronger than intraspecific competition. A moving area of overlap may result when one species is a superior competitor. In the Carduus system, our model suggests that invasional interference will lead to lower levels of each species when together, but a similar net level of thistle invasion due to the similarity of intra- and interspecific competition. Thus, invasional interference may have important implications for the distribution and management of invasive species.