Competitive interactions between co-occurring invasive species can have detrimental impacts on native community composition and cause counter-effective responses to management. Targeted removal of one invader may allow for the release of a subdominant invader, causing a secondary invasion. The goal of this research was to elucidate competitive dynamics between Bromus tectorum and Ventenata dubia, two invasive winter annual grasses found in the western United States. We quantified the impacts of 1) intraspecific competition on B. tectorum and V. dubia as density of conspecifics increased and 2) interspecific competition between the two at varying proportions. The two species were grown at increasing densities and proportions (addition series), over 10 weeks in a greenhouse. At the end of the growth period, aboveground biomass was harvested and weighed. We derived the intraspecific and interspecific competitive effects on each species with a non-linear analysis and used these coefficients to determine Relative Competitive Ability. Bromus tectorum was negatively impacted by intraspecific and interspecific competition. Similarly, V. dubia biomass was negatively impacted by intraspecific competition, as well as increasing density of B. tectorum. This suggests that replacement of B. tectorum by V. dubia is unlikely to be caused by aboveground competition alone, but if B. tectorum were reduced V. dubia could be released. Understanding the competitive interactions between these species provides insight into invasive species impacts and management. This approach will become increasingly valuable to apply as climate and other global change factors alter vegetation communities and species interactions.