Labor monitoring is crucial in modern health care, as it can be used to detect (and help avoid) significant problems with the fetus. In this article we focus on detecting hypoxia (or oxygen deprivation), a very serious condition that can arise from different pathologies and can lead to lifelong disability and death. We present a novel approach to hypoxia detection based on recordings of the uterine pressure and fetal heart rate, which are obtained using standard labor monitoring devices. The key idea is to learn models of the fetal response to signals from its environment. Then, we use the parameters of these models as attributes in a binary classification problem. A running count of pathological classifications over several time periods is taken to provide the current label for the fetus. We use a unique database of real clinical recordings, both from normal and pathological cases. Our approach classifies correctly more than half the pathological cases, 1.5 hours before delivery. These are cases that were missed by clinicians; early detection of this type would have allowed the physician to perform a Cesarean section, possibly avoiding the negative outcome.