Despite obvious impacts of nonnative species in many ecosystems, the long-term outcome of competition between native and exotic species often remains unclear. Demographic models can resolve the outcome of competition between native and exotic species and provide insight into conditions favoring exclusion vs. coexistence. California grasslands are one of the most heavily invaded ecosystems in North America. Although California native perennial bunchgrasses are thought to be restricted to a fraction of their original abundance, the eventual outcome of competition with invasive European annual grasses at a local scale (competitive exclusion, stable persistence, or priority effects) remains unresolved. Here, we used a two-species discrete time population growth model to predict the outcome of competition between exotic annual and native perennial grasses in California, and to determine the demographic traits responsible for the outcome. The model is parameterized with empirical data from several field experiments. We found that, once introduced, annual grasses persist stably with little uncertainty. Although perennial grasses are competitively excluded on average, the most likely range of model predictions also includes stable coexistence with annual grasses. As for many other perennial plants, native bunchgrass population growth is highly sensitive to the survival of adults. Management interventions that improve perennial adult survival are likely to be more effective than those that reduce exotic annual seed production or establishment, reduce competition, or increase perennial seedling establishment. Further empirical data on summer survival of bunchgrass adults and competitive effects of annuals on perennials would most improve model predictions because they contribute most to the uncertainty in the predicted outcome for the perennial grass. This work demonstrates how demographic approaches can clarify the outcome of competition between native and exotic species, identify key targets for future empirical work, and predict the effectiveness of management interventions. Such studies are critical both for understanding the impacts of invasion and for targeting management responses that maximize the benefit to native species.