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Labor and delivery are routinely monitored electronically with sensors that measure and record maternal uterine pressure (UP) and fetal heart rate (FHR), a procedure referred to as cardiotocography (CTG). Delay or failure to recognize abnormal patterns in these recordings can result in a failure to prevent fetal injury. We address the challenging problem of interpreting intrapartum CTG in a novel way by modeling the dynamic relationship between UP (as an input) and FHR (as an output). We use a nonparametric approach to estimate the dynamics in terms of an impulse response function (IRF). We apply singular value decomposition to suppress noise, IRF delay, and memory estimation to identify the temporal extent of the response and surrogate testing to assess model significance. We construct models for a database of CTG recordings labeled by outcome, and compare the models during the last 3 h of labor as well as across outcome classes. The results demonstrate that the UP-FHR dynamics can be successfully modeled as an input-output system. Models for pathological cases had stronger, more delayed, and more predictable responses than those for normal cases. In addition, the models evolved in time, reflecting a clinically plausible evolution of the fetal state due to the stress of labor.