Recording of maternal uterine pressure (UP) and fetal heart rate (FHR) during labour and delivery is a procedure referred to as cardiotocography (CTG). We model this as an input-output system using a nonparametric approach to estimate its dynamics in terms of an impulse response function (IRF). In this paper, we incorporate IRF delay and memory detection into our identification methods to estimate the temporal extent of the IRF as well as its dynamics. Our models showed that pathological cases had stronger, later and more predictable responses.