We used eye-tracking to investigate lexical processing in aphasic participants by examining the fixation time course for rhyme (e.g., "carrot-parrot") and cohort (e.g., "beaker-beetle") competitors. Broca's aphasic participants exhibited larger rhyme competition effects than age-matched controls. A re-analysis of previously reported data (Yee, Blumstein, & Sedivy, 2008) confirmed that Wernicke's aphasic participants exhibited larger cohort competition effects. Individual-level analyses revealed a negative correlation between rhyme and cohort competition effect size across both groups of aphasic participants. Computational model simulations were performed to examine which of several accounts of lexical processing deficits in aphasia might account for the observed effects. Simulation results revealed that slower deactivation of lexical competitors could account for increased cohort competition in Wernicke's aphasic participants; auditory perceptual impairment could account for increased rhyme competition in Broca's aphasic participants; and a perturbation of a parameter controlling selection among competing alternatives could account for both patterns, as well as the correlation between the effects. In light of these simulation results, we discuss theoretical accounts that have the potential to explain the dynamics of spoken word recognition in aphasia and the possible roles of anterior and posterior brain regions in lexical processing and cognitive control.