Summary1. Many species prioritized for bioenergy crop development possess traits associated with invasiveness, necessitating a priori efforts by ecologists to identify species or cultivars with minimal invasive potential. The grass Miscanthus 9 giganteus Greef et Deu ex Hodkinson et Renvoize is a candidate for biomass production in the northern US maize belt, with both sterile and fertile varieties commercially available in the near future. Prior to widespread deployment, the invasive potential of both varieties must be quantified. 2. Using M. 9 giganteus demographic and seed dispersal data, we parameterized an age-/stage-structured integrodifference equation model to estimate potential spread rates of sterile and fertile M. 9 giganteus. We identified thresholds for reproductive parameters, above which population numbers and space occupied are likely to increase. Our simulations considered lateral spread of M. 9 giganteus but not dispersal of rhizome fragments. 3. When clonal recruitment is absent, population growth rate for sterile M. 9 giganteus is projected to be slightly <1 (k = 0Á979), indicating gradual population decline over the long term. A sterile M. 9 giganteus population may increase in numbers and space under certain conditions: annually rhizome sprouting must be >20% and rhizome production must be ! 1 per plant. The relatively slow spread rates (0-0Á09 m year À1 ) estimated for sterile M. 9 giganteus would not apply in scenarios where rhizomes were dispersed long distance. For a fertile M. 9 giganteus genotype, even low rates of seed viability and survival, seedling survival and seed germination support rapidly expanding populations. 4. Synthesis and applications. Spatial demographic models offer a powerful tool for quantifying risk of invasive spread by bioenergy crops. Our results suggest that sterile and fertile cultivars of M. 9 giganteus have markedly different invasive potential and therefore should be considered separately in management and policy decisions. Feral populations of sterile M. 9 giganteus would need to experience frequent and severe disturbance to pose a significant invasion risk, indicating that they should be grown well away from riparian areas prone to streambank scouring. In contrast, cultivars of M. 9 giganteus bearing fertile seed may be very difficult, if not impossible, to contain.