The ability to express and learn temporal sequences is an essential part of learning and memory. Learned temporal sequences are expressed in multiple brain regions and as such there may be common design in the circuits that mediate it. This work proposes a substrate for such representations, via a biophysically realistic network model that can robustly learn and recall discrete sequences of variable order and duration. The model consists of a network of spiking leaky-integrate-and-fire model neurons placed in a modular architecture designed to resemble cortical microcolumns. Learning is performed via a learning rule with "eligibility traces", which hold a history of synaptic activity before being converted into changes in synaptic strength upon neuromodulator activation. Before training, the network responds to incoming stimuli, and contains no memory of any particular sequence. After training, presentation of only the first element in that sequence is sufficient for the network to recall an entire learned representation of the sequence. An extended version of the model also demonstrates the ability to successfully learn and recall non-Markovian sequences. This model provides a possible framework for biologically realistic sequence learning and memory, and is in agreement with recent experimental results, which have shown sequence dependent plasticity in sensory cortex.So long as time flows in one direction, nature itself is fundamentally sequential. To operate in this reality, the brain needs to think, plan, and take action in a temporally ordered fashion. When you sing a song, hit a baseball, or even utter a word, you are engaging in sequential activity. More accurately, you are engaging in sequential recall of a learned activity -your actions not only have *a* temporal order and duration, but *the* temporal order and duration which you observed.Hence, the question of how sequence representations are learned, stored, and recalled is of fundamental importance to neuroscience. Recent evidence has shown that such learned representations can exist in cortical circuits 1-5 , begging the question: how are these circuits constructed, and how can such representations be learned?To address these questions, we introduce a biophysically realistic modular network with an eligibility trace-based learning rule that can robustly learn and recall both the order and duration of elements in a sequence. Although the model's construction is based upon recent experimental observations in visual cortex 1-3 , utilizing observed cell types 6-8 and laminar structure 9,10 , many of its key aspects (modularity, heterogenous representations) are illustrative of general principles of sequence learning. The ability of the network to learn both duration and order, along with its use of a learning rule that bypasses the need for constant and explicit targets, differs from most historical and contemporary models of sequence learning [11][12][13][14][15][16][17][18][19][20] . We also present an extended formulation of the model, which is capabl...