Neuroimaging studies of cognition have typically been designed to identify brain regions that are active during a cognitive process. However, identifying how brain regions interact may be equally important. In a recent study we found that the pattern of activation associated with a semantic task differed depending on how subjects made a response, suggesting that there was an interaction between the neural systems underlying response mode and semantic processing (J. M. Jennings et al., 1997, NeuroImage 5, 229-239). This result raises two important questions, which we examined here: (1) How did the regions underlying semantic performance influence one another, or interact, to produce a different pattern of activation in each case? (2) What can be learned about the neurobiology of semantic processing when different regions are identified as a function of response? We addressed these questions using structural equation modeling. This technique produced functional network models representing the effect of different regions on each other during the semantic task for each response. A common network of regions associated with semantic processing was observed and included the left inferior frontal and left superior temporal cortices, with other regions brought into that network depending on response (e.g., right middle frontal). Moreover, changes in the influences among these regions across response condition predicted the pattern of activation found previously. These results show how an arbitrary response can affect the neural pathways associated with a cognitive process, likely due to the parallel and reentrant organization of the brain, and emphasize the importance of examining functional connections when studying cognition.