Several mechanisms have been proposed to explain the success of invasive species in new environments. A species may become invasive when a new site provides the potential for positive rates of population growth. This may be the case of several Agave species introduced to Spain in the 1940s. In this paper we document factors that promote large increases of populations of these species, and their effects on native plant communities in two sites of SE Spain. Results showed higher rhizome and bulbil production, and higher establishment rates by agaves in sandy soils than in clay soils. In their native habitats, agaves have low establishment rates and sandy soils are rare. This suggests that sandy soils are an opportunity which releases the clonal reproduction of Agave. The effects of agaves on the physiological performance and reproduction of native species were negative, positive or neutral, depending on the size and rooting depth of neighbours. Assemblages of native species growing within Agave stands had lower diversity than non-invaded sites. Our data show that Agave stands have positive growth rates in SE Spain, and suggest that sandy soils are a niche dimension enhancing the invasion in these new habitats.