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Objectives. Brain-machine interfaces (BMIs) aim to help people with motor disabilities by interpreting brain signals into motor intentions using advanced signal processing methods. Currently, BMI users require intensive training to perform a pre-defined task, not to mention learning a new task. Thus, it is essential to understand neural information pathways among the cortical areas in task learning to provide principles for designing BMIs with learning abilities. We propose to investigate the relationship between the medial prefrontal cortex (mPFC) and primary motor cortex (M1), which are actively involved in motor control and task learning, and show how information is conveyed in spikes between the two regions on a single-trial basis by computational models. Approach. We are interested in modeling the functional relationship between mPFC and M1 activities during task learning. Six Sprague Dawley rats were trained to learn a new behavioral task. Neural spike data was recorded from mPFC and M1 during learning. We then implement the generalized linear model, the second-order generalized Laguerre-Volterra model, and the staged point-process model to predict M1 spikes from mPFC spikes across multiple days during task learning. The prediction performance is compared across different models or learning stages to reveal the relationship between mPFC and M1 spike activities. Main results. We find that M1 neural spikes can be well predicted from mPFC spikes on the single-trial level, which indicates a highly correlated relationship between mPFC and M1 activities during task learning. By comparing the performance across models, we find that models with higher nonlinear capacity perform significantly better than linear models. This indicates that predicting M1 activity from mPFC activity requires the model to consider higher-order nonlinear interactions beyond pairwise interactions. We also find that the correlation coefficient between the mPFC and M1 spikes increases during t