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Many studies obtained reliable individual differences in speed of information processing (SIP) as measured by elementary cognitive tasks (ECTs). ECTs usually employ response times (RT) as measure of SIP, but different ECTs target different cognitive processes (e.g., simple or choice reaction, inhibition). Here we used modified versions of the Hick and the Eriksen Flanker task to examine whether these tasks assess dissociable or common aspects of SIP. In both tasks, task complexity was systematically varied across three levels. RT data were collected from 135 participants. Applying fixed-links modeling, RT variance increasing with task complexity was separated from RT variance unchanging across conditions. For each task, these aspects of variance were represented by two independent latent variables. The two latent variables representing RT variance not varying with complexity of the two tasks were virtually identical (r = .83). The latent variables representing increasing complexity in the two tasks were also highly correlated (r = .72) but clearly dissociable. Thus, RT measures contain both task-unspecific, person-related aspects of SIP as well as task-specific aspects indicating the cognitive processes manipulated with the respective task. Separating these aspects of SIP facilitates the interpretation of individual differences in RT.