Recently, there has been a redirection of research efforts toward the exploration of the role of hemispheric lateralization in determining Simon effect asymmetries. The present study aimed at implementing a connectionist model that simulates the cognitive mechanisms implied by such asymmetries, focusing on the underlying neural structure. A left-lateralized response-selection mechanism was implemented alone (Experiment 1) or along with a right-lateralized automatic attention-orienting mechanism (Experiment 2). It was found that both models yielded Simon effect asymmetries. However, whereas the first model showed a reversed pattern of asymmetry compared with human, real data, the second model's performance strongly resembled human Simon effect asymmetries, with a significantly greater right than left Simon effect. Thus, a left-side bias in the response-selection mechanism produced a left-side biased Simon effect, whereas a right-side bias in the attention system produced a right-side biased Simon effect. In conclusion, results showed that the bias of the attention system had a larger impact than the bias of the response-selection mechanism in producing Simon effect asymmetries.