Cognitive neuroscience currently conflates the study of serial responses (e.g., delay match to sample/nonsample, n-back) with the study of sequential operations. In this essay, our goal is to define and disentangle the latter, termed abstract cognitive task sequences (ACTS). Existing literatures address tasks requiring serial events, including procedural learning of implicit motor responses, statistical learning of predictive relationships, and judgments of attributes. These findings do not describe the behavior and underlying mechanism required to succeed at remembering to evaluate color, then shape; or to multiply, then add. A new literature is needed to characterize these sorts of second-order cognitive demands of studying a sequence of operations. Our second goal is to characterize gaps in knowledge related to ACTS that merit further investigation. In the following sections, we define more precisely what we mean by ACTS and suggest research questions that further investigation would be positioned to address.