A process of response inhibition is often held to be recruited in situations where it is necessary to withhold or inhibit a prepotent response. Individual differences in the efficacy of this function have been held to underlie individual differences in behaviour on tasks such as the Stroop colour-naming task and the stop-signal task. These claims, however, have been supported only with correlational analyses and informal argument. This paper considers the operationalisation of response inhibition by exploring existing mathematical and process models of both the Stroop and stop-signal tasks. We identify parameters that might underlie individual differences in the performance of the tasks and consider potential relations between those parameters. It is shown that (a) at least three potential inter-relations between parameters of the task models may lead to inter-task correlations, and (b) the observed correlations arise when attentional bias parameters in the models are equated but not when inhibition parameters are equated. We conclude that the ascription of such correlations to a process of response inhibition is premature.