Many classic decision-making paradigms require animals to select between alternative choices by accumulating evidence over time. Traditional models of decision-making posit that such accumulation is reflected in the activity of single neurons whose activity ramps up or down with evidence. However, recent experiments suggest that, in many settings, neurons do not exhibit persistent, ramping activity but rather are transiently and sequentially activated. Motivated by experiments in a navigation-based, accumulation of evidence task in which sequential activity is observed across multiple regions of neocortex, hippocampus, and striatum, we here propose two classes of networks that accumulate evidence in their sequential activity. First, we create a planar “bump attractor” model in which individual neurons are tuned to particular values of position and evidence, and the set of active neurons shifts along one axis with changes in evidence and along the other axis with changes in position. This model predicts unimodal tuning curves for individual neurons when plotted as a function of evidence and position, as has been observed in the response profiles for neurons in the hippocampus. Second, we develop a model consisting of two mutually inhibitory chains of neurons, in which each chain receives evidence cues for one of two alternative choices. Evidence for a given choice increases activity in one chain while decreasing activity in the other, while activity progresses forward in each chain with position. This model predicts tuning curves that are tuned to a specific position and that increase or decrease monotonically with evidence, as observed in our preliminary recordings in the anterior cingulate cortex. Overall, this work represents the first models of how circuits displaying sequential activity can solve accumulation-of-evidence decision-making tasks, and makes predictions about different underlying computational architectures in different brain regions.